{VERSION 7 1 "Linux" "7.1" } {USTYLETAB {PSTYLE "Ordered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 } {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output " -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 3 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS S erif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 12 40 120 40 1 2 2 2 2 2 1 2 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered \+ List 4" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 2 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "H eading 2" -1 4 1 {CSTYLE "" -1 -1 "MS Serif" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courie r" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered Li st 2" -1 204 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "Equation Label" -1 200 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Couri er" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Ser if" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 203 38 "Bevezet\303\251s a matem atik\303\241ba" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 204 18 "J\303\241rai \+ Antal" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 201 69 "Ezek a programok csak \+ szeml\303\251ltet\303\251sre szolg\303\241lnak." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 11 "1. Halmazok" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 35 "2. Term\303\251s zetes sz\303\241mok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 53 "3. A sz\303\241mfogalom b\305\221v\303\2 55t\303\251se" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT 205 24 "4. V\303\251ges halmazok" }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 27 "5. V\303\251gtelen halmazok" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 205 28 "6 . Sz\303\241melm\303\251let" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 205 28 "7. Gr\303\241felm\30 3\251let" }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 45 "7.1. Ir\303\241ny\303\255tatlan gr\303\2 41fok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 48 "7.1.1. Ir\303\241ny\303\255tatlan gr\303\241fok." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(netwo rks);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7hoI)acycpolyG6\"I(addedgeGF$I* addvertexGF$I*adjacencyGF$I)allpairsGF$I)ancestorGF$I)arrivalsGF$I-bic omponentsGF$I)charpolyGF$I*chrompolyGF$I+complementGF$I)completeGF$I+c omponentsGF$I(connectGF$I-connectivityGF$I)contractGF$I*countcutsGF$I+ counttreesGF$I%cubeGF$I&cycleGF$I*cyclebaseGF$I)daughterGF$I*degreeseq GF$I'deleteGF$I+departuresGF$I)diameterGF$I&dinicGF$I+djspantreeGF$I-d odecahedronGF$I%drawGF$I'draw3dGF$I*duplicateGF$I&edgesGF$I%endsGF$I(e weightGF$I%flowGF$I)flowpolyGF$I(fundcycGF$I)getlabelGF$I&girthGF$I&gr aphGF$I*graphicalGF$I&gsimpGF$I'gunionGF$I%headGF$I,icosahedronGF$I*in cidenceGF$I)incidentGF$I)indegreeGF$I'induceGF$I)isplanarGF$I*maxdegre eGF$I'mincutGF$I*mindegreeGF$I*neighborsGF$I$newGF$I+octahedronGF$I*ou tdegreeGF$I%pathGF$I)petersenGF$I'randomGF$I%rankGF$I)rankpolyGF$I.sho rtpathtreeGF$I%showGF$I'shrinkGF$I%spanGF$I)spanpolyGF$I)spantreeGF$I% tailGF$I,tetrahedronGF$I*tuttepolyGF$I(vdegreeGF$I)verticesGF$I%voidGF $I(vweightGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "new(G1):ad dvertex(\{v1,v2,v3,v4,v5\},G1);\n" }{MPLTEXT 1 0 66 "addedge([\{v1,v2 \},\{v1,v2\},\{v1,v4\},\{v3,v4\},\{v4,v4\}],G1);\n" }{MPLTEXT 1 0 25 " edges(G1);vertices(G1);\n" }{MPLTEXT 1 0 14 "ends(e2,G1);\n" }{MPLTEXT 1 0 22 "edges(\{v1,v2\},G1);\n" }{MPLTEXT 1 0 34 "incident(v1,G1);inc ident(v5,G1);\n" }{MPLTEXT 1 0 34 "neighbors(v1,G1);neighbors(v4,G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'I#v1G6\"I#v2GF$I#v3GF$I#v5GF$I#v4GF $" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'I#e1G6\"I#e2GF$I#e3GF$I#e4GF$I#e5 GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<'I#e1G6\"I#e2GF$I#e3GF$I#e4GF$I# e5GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<'I#v1G6\"I#v2GF$I#v3GF$I#v5GF$ I#v4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<$I#v1G6\"I#v2GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<$I#e1G6\"I#e2GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I#e1G6\"I#e2GF$I#e3GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "%#%?G" } }{PARA 11 "" 1 "" {XPPMATH 20 "<$I#v2G6\"I#v4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I#v1G6\"I#v3GF$I#v4GF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "vdegree(v1,G1);vdegree(v4,G1);vdegree(v5,G1);degreese q(G1);mindegree(G1);maxdegree(G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7'\"\"!\"\"\"\"\"# \"\"$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "show(G 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6#71/I&_Tail G6\"-F#6#7\"/I,_CounttreesGF)F./I*_VerticesGF)<'I#v1GF)I#v2GF)I#v3GF)I #v5GF)I#v4GF)/I)_VweightGF)-F#6$I'sparseGF)F,/I+_EdgeIndexGF)-F#6$I*sy mmetricGF)7&/6$F4F6<#I#e4GF)/6$F2F6<#I#e3GF)/F6<#I#e5GF)/6$F2F3<$I#e1G F)I#e2GF)/I/_EconnectivityGF)FS/I*_EmaxnameGF)\"\"&/I&_HeadGF)F*/I)_Ew eightGF)-F#6#7'/FE\"\"\"/FPFin/FLFin/FQFin/FIFin/I'_EdgesGF)<'FPFQFIFE FL/I+_NeighborsGF)-F#6#7'/F6<%F2F4F6/F5<\"/F3<#F2/F4<#F6/F2<$F3F6/I(_S tatusGF)<$I+MULTIGRAPHGF)I&LOOPSGF)/I&_EndsGF)-F#6#7'/FE<$F4F6/FP<$F2F 3/FLF]p/FQF]q/FI<$F2F6/I._BicomponentsGF)Fcq/I+_CountcutsGF)Feq" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "G:=void(10):vertices(G);edge s(G);\n" }{MPLTEXT 1 0 69 "addedge([\{1,2\},\{2,3\},\{3,4\}],names=[ci ca,alma,kutya],G);show(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<,\"\"\"\" \"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "%#%?G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%I%cicaG6\"I%alma GF$I&kutyaGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6# 7//I&_TailG6\"-F#6#7\"/I,_CounttreesGF)F./I*_VerticesGF)<,\"\"\"\"\"# \"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5/I)_VweightGF)-F#6$I'sparseGF)F ,/I+_EdgeIndexGF)-F#6$I*symmetricGF)7%/6$F4F5<#I&kutyaGF)/6$F3F4<#I%al maGF)/6$F2F3<#I%cicaGF)/I/_EconnectivityGF)FT/I&_HeadGF)F*/I)_EweightG F)-F#6#7%/FNF2/FJF2/FRF2/I'_EdgesGF)<%FRFNFJ/I+_NeighborsGF)-F#6#7,/F2 <#F3/F3<$F2F4/F4<$F3F5/F6<\"/F5<#F4/F8Fho/F7Fho/F;Fho/F9Fho/F:Fho/I&_E ndsGF)-F#6#7%/FN<$F3F4/FJ<$F4F5/FR<$F2F3/I._BicomponentsGF)F\\q/I+_Cou ntcutsGF)F^q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "G:=petersen ():draw(G);degreeseq(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" } {GLPLOT2D 400 400 400 {PLOTDATA 2 "68-%*AXESSTYLEG6#%%NONEG-%'POINTSG6 #7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q\"66\"-F(6#7 $$\"+Q*p,4$!#5$\"+l^c5&*F?-F06$7$$\"+Q*p,4&F?F@Q\"8F9-F(6#7$$!+]*p,4)F ?$\"+9D&y(eF?-F06$7$$!+&*p,45!\"*$\"1-++9D&y(eF5Q#10F9-F(6#7$$!+M*p,4) F?$!+PD&y(eF?-F06$7$$!2-++I*p,45F5FgnQ\"7F9-F(6#7$$\"+l*p,4$F?$!+c^c5& *F?-F06$7$$\"1+++l*p,4&F5FdoQ\"9F9-F(6#7$$\"+nmmm;FTF.-F06$7$$\"+nmmm= FTF6Q\"1F9-F(6#7$$\"+IKG]^F?$\"+%>%4&e\"FT-F06$7$$\"1-++IKG]rF5F\\qQ\" 2F9-F(6#7$$!+e;O[8FT$\"+d3U'z*F?-F06$7$$!2-++!e;O[:F5FiqQ\"3F9-F(6#7$$ !+c;O[8FT$!+&*3U'z*F?-F06$7$$!2-++glh$[:F5$!1+++&*3U'z*F5Q\"4F9-F(6#7$ $\"+vKG]^F?$!+$>%4&e\"FT-F06$7$$\"+vKG]rF?$!2-++I>%4&e\"F5Q\"5F9-%'CUR VESG627$F^pFip7$FipFfq7$FfqFcr7$FcrFbs7$F^pFbs7$F*FZ7$FZF<7$F7.1.2. Feladat." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.1.3. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.1.4. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.1.5. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "*7.1.6. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 40 "7.1 .7. Gr\303\241fok izomorfi\303\241ja." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 8 "7.1.8 . P" }{TEXT 207 20 "\303\251ld\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "G21:=complete(5):draw (G21);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "61-%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--F (6#7$$\"+Q*p,4$!#5$\"+l^c5&*F4-F(6#7$$!+]*p,4)F4$\"+9D&y(eF4-F(6#7$$!+ M*p,4)F4$!+PD&y(eF4-F(6#7$$\"+l*p,4$F4$!+c^c5&*F4-%'CURVESG6$7$F*F@-%& COLORG6&%$RGBG$F-!\"\"$\"#5FUFT-FM6$7$F1FGFP-FM6$7$F*F9FP-%%TEXTG6$7$$ \"2-++++++?\"!#;FTQ\"16\"-Fin6$7$$\"+Q*p,4&F4F5Q\"2F`o-Fin6$7$$!+&*p,4 5!\"*$\"1-++9D&y(eF^oQ\"3F`o-Fin6$7$$!2-++I*p,45F^oFCQ\"4F`o-Fin6$7$$ \"1+++l*p,4&F^oFJQ\"5F`o-FM6*7$F*F17$F*FG7$F1F97$F1F@7$F9F@7$F9FG7$F@F G-FQ68FSFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFT" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve \+ 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curv e 12" "Curve 13" "Curve 14" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 40 "7.1 .9. Gr\303\241fok Descartes-szorzata." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 18 "->7. 1.10. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.11. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.12. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 35 "7.1.13. P\303\2 41ros gr\303\241fok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "new(G22):addvertices([H1,H2,H3,K1,K2,K3], G22);connect(\{H1,H2,H3\},\{K1,K2,K3\},G22);draw(G22);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(I#H1G6\"I#H2GF$I#H3GF$I#K2GF$I#K1GF$I#K3GF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6+I#e1G6\"I#e2GF$I#e3GF$I#e4GF$I#e5GF$I# e6GF$I#e7GF$I#e8GF$I#e9GF$" }}{PARA 13 "" 1 "" {TEXT 208 0 "" } {GLPLOT2D 400 400 400 {PLOTDATA 2 "60-%*AXESSTYLEG6#%%NONEG-%'POINTSG6 #7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q#H16\"-F(6#7 $$\"+-+++]!#5$\"+PSDg')F?-F06$7$$\"+-+++qF?F@Q#H2F9-F(6#7$$!+(******* \\F?$\"+SSDg')F?-F06$7$$!+(*******pF?$\"*/a-m)!\"*Q#H3F9-F(6#7$$F7F-$ \"+&QKz*e!#>-F06$7$$!2-++++++?\"F5$\"1-++&QKz*e!#DQ#K1F9-F(6#7$$!+2+++ ]F?$!+MSDg')F?-F06$7$$!+2+++qF?FgoQ#K2F9-F(6#7$$\"+\"*******\\F?$!+VSD g')F?-F06$7$$\"+\"*******pF?$!1+++VSDg')F5Q#K3F9-%'CURVESG6,7$F*Fdo7$F *FZ7$F*Fap7$F%$RGBGF6$ \"#5F7F6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Cu rve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "C urve 11" "Curve 12" "Curve 13" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "G:=complete(3,3):draw(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "60-%*AXESSTYLEG6#%% NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-! \"\"Q\"16\"-F(6#7$$\"+-+++]!#5$\"+PSDg')F?-F(6#7$$!+(*******\\F?$\"+SS Dg')F?-F(6#7$$F7F-$\"+&QKz*e!#>-F(6#7$$!+2+++]F?$!+MSDg')F?-F(6#7$$\"+ \"*******\\F?$!+VSDg')F?-%'CURVESG6,7$F*FR7$F*FK7$F*FY7$F%$RGBGF6$\"#5F7F6F6FhoF6F6FhoF6F6FhoF6F 6FhoF6F6FhoF6F6FhoF6F6FhoF6F6FhoF6-F06$7$$\"+-+++qF?F@Q\"2F9-F06$7$$!+ (*******pF?$\"*/a-m)!\"*Q\"3F9-F06$7$$!2-++++++?\"F5$\"1-++&QKz*e!#DQ \"4F9-F06$7$$!+2+++qF?FUQ\"5F9-F06$7$$\"+\"*******pF?$!1+++VSDg')F5Q\" 6F9" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Cur ve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Cur ve 10" "Curve 11" "Curve 12" "Curve 13" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.14. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 31 "7.1.15. R\303\251szgr\303\241f." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "show(G);" }}{PARA 11 " " 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6#71/I&_TailG6\"-F#6#7\"/I,_C ounttreesGF)F./I*_VerticesGF)<(\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'/I)_Vwei ghtGF)-F#6$I'sparseGF)F,/I+_EdgeIndexGF)-F#6$I*symmetricGF)7+/6$F2F6<# I#e2GF)/6$F2F5<#I#e1GF)/6$F3F6<#I#e5GF)/6$F4F7<#I#e9GF)/6$F3F5<#I#e4GF )/6$F3F7<#I#e6GF)/6$F4F5<#I#e7GF)/6$F4F6<#I#e8GF)/6$F2F7<#I#e3GF)/I/_E connectivityGF)Fbo/I*_EmaxnameGF)\"\"*/I&_HeadGF)F*/I)_EweightGF)-F#6# 7+/FVF2/FRF2/FhnF2/FJF2/FNF2/FZF2/FFF2/F\\oF2/F`oF2/I'_EdgesGF)<+FJFFF `oFVFNFZFhnF\\oFR/I+_NeighborsGF)-F#6#7(/F2<%F5F6F7/F3F_q/F4F_q/F6<%F2 F3F4/F5Fcq/F7Fcq/I(_StatusGF)<$I'SIMPLEGF)I*BIPARTITEGF)/I&_EndsGF)-F# 6#7+/FV<$F3F5/FR<$F4F7/Fhn<$F4F5/FJ<$F2F5/FN<$F3F6/FZ<$F3F7/FF<$F2F6/F \\o<$F4F6/F`o<$F2F7/I._BicomponentsGF)Fcs/I+_CountcutsGF)Fes" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "delete(\{e4\},delete(\{1\},G )):vertices(%);edges(%%);draw(%%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "< '\"\"#\"\"$\"\"%\"\"&\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "<'I#e5G6\" I#e6GF$I#e7GF$I#e8GF$I#e9GF$" }}{PARA 13 "" 1 "" {TEXT 208 0 "" } {GLPLOT2D 400 400 400 {PLOTDATA 2 "6.-%*AXESSTYLEG6#%%NONEG-%'POINTSG6 #7$$\"\"\"\"\"!$F-F--F(6#7$$\"+Q*p,4$!#5$\"+l^c5&*F4-F(6#7$$!+]*p,4)F4 $\"+9D&y(eF4-F(6#7$$!+M*p,4)F4$!+PD&y(eF4-F(6#7$$\"+l*p,4$F4$!+c^c5&*F 4-%'CURVESG6(7$F*F@7$F1FG7$F*FG7$F1F97$F1F@-%&COLORG62%$RGBG$F-!\"\"$ \"#5FYFXFXFZFXFXFZFXFXFZFXFXFZFX-%%TEXTG6$7$$\"2-++++++?\"!#;FXQ\"26\" -Fgn6$7$$\"+Q*p,4&F4F5Q\"3F^o-Fgn6$7$$!+&*p,45!\"*$\"1-++9D&y(eF\\oQ\" 4F^o-Fgn6$7$$!2-++I*p,45F\\oFCQ\"5F^o-Fgn6$7$$\"1+++l*p,4&F\\oFJQ\"6F^ o" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "show(G1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protected G6#71/I&_TailG6\"-F#6#7\"/I,_CounttreesGF)F./I*_VerticesGF)<'I#v1GF)I# v2GF)I#v3GF)I#v5GF)I#v4GF)/I)_VweightGF)-F#6$I'sparseGF)F,/I+_EdgeInde xGF)-F#6$I*symmetricGF)7&/6$F4F6<#I#e4GF)/6$F2F6<#I#e3GF)/F6<#I#e5GF)/ 6$F2F3<$I#e1GF)I#e2GF)/I/_EconnectivityGF)FS/I*_EmaxnameGF)\"\"&/I&_He adGF)F*/I)_EweightGF)-F#6#7'/FE\"\"\"/FPFin/FLFin/FQFin/FIFin/I'_Edges GF)<'FPFQFIFEFL/I+_NeighborsGF)-F#6#7'/F6<%F2F4F6/F5<\"/F3<#F2/F4<#F6/ F2<$F3F6/I(_StatusGF)<$I+MULTIGRAPHGF)I&LOOPSGF)/I&_EndsGF)-F#6#7'/FE< $F4F6/FP<$F2F3/FLF]p/FQF]q/FI<$F2F6/I._BicomponentsGF)Fcq/I+_Countcuts GF)Feq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "new(G3):addverte x(\{v1,v2,v3,v4\},G3);addedge([\{v1,v2\},\{v2,v3\},\{v1,v4\},\{v2,v4\} ],G3);draw(G3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&I#v1G6\"I#v2GF$I#v3 GF$I#v4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&I#e1G6\"I#e2GF$I#e3GF$I# e4GF$" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6/-%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--% %TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q#v16\"-F(6#7$$!+3Q.^?!#>F+-F06$7$$ !+-+++?!#5$\"#5F7Q#v2F9-F(6#7$$F7F-$!+:w1-TF?-F06$7$$!2-++++++?\"F5$!% -T!#8Q#v3F9-F(6#7$$\"+A95`hF?FL-F06$7$$\"+1+++?FE$FEF7Q#v4F9-%'CURVESG 6$7$F*F<-%&COLORG6&%$RGBGF6FFF6-F_o6$7$F \+ " 0 "" {MPLTEXT 1 0 21 "draw(complement(G3));" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6--%*AXESSTYLEG6#%% NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-! \"\"Q#v16\"-F(6#7$$!+3Q.^?!#>F+-F06$7$$!+-+++?!#5$\"#5F7Q#v2F9-F(6#7$$ F7F-$!+:w1-TF?-F06$7$$!2-++++++?\"F5$!%-T!#8Q#v3F9-F(6#7$$\"+A95`hF?FL -F06$7$$\"+1+++?FE$FEF7Q#v4F9-%'CURVESG6$7$FKFZ-%&COLORG6&%$RGBGF6FFF6 -F_o6$7$F*FKFbo" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "C urve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "C urve 9" "Curve 10" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "induce(\{v2,v3,v4\},G3):draw(%);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6+-%*AXESSTYLEG6#%% NONEG-%%TEXTG6$7$$!+0+++q!#5$\"+NSDg')F-Q#v36\"-%'POINTSG6#7$$\"\"\"\" \"!$F8F8-F(6$7$$\"2-++++++?\"!#;$F8!\"\"Q#v2F1-F36#7$$!+0+++]F-F.-F36# 7$$!+*)******\\F-$!+WSDg')F--F(6$7$$!+*)******pF-FMQ#v4F1-%'CURVESG6$7 $F5FE-%&COLORG6&%$RGBGF@$\"#5FAF@-FV6$7$F5FJFY" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" " Curve 6" "Curve 7" "Curve 8" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "induce(\{e2,e1,e4\},G3):draw(%);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6.-%*AXESSTYLEG 6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$ F-!\"\"Q#v16\"-F(6#7$$!+3Q.^?!#>F+-F06$7$$!+-+++?!#5$\"#5F7Q#v2F9-F(6# 7$$F7F-$!+:w1-TF?-F06$7$$!2-++++++?\"F5$!%-T!#8Q#v3F9-F(6#7$$\"+A95`hF ?FL-F06$7$$\"+1+++?FE$FEF7Q#v4F9-%'CURVESG6$7$F*F<-%&COLORG6&%$RGBGF6F FF6-F_o6$7$F7.1.16. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.17. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.18. Felad at." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 64 "7.1.19. S\303\251t\303\241k, vonalak, ut ak, k\303\266r\303\266k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "G4:=void(9):addedge(Path(1,2,3,4,5, 6,7,3,8,9,8),G4);show(G4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,I#e1G6\" I#e2GF$I#e3GF$I#e4GF$I#e5GF$I#e6GF$I#e7GF$I#e8GF$I#e9GF$I$e10GF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6#71/I&_TailG6\"-F# 6#7\"/I,_CounttreesGF)F./I*_VerticesGF)<+\"\"\"\"\"#\"\"$\"\"%\"\"&\" \"'\"\"(\"\")\"\"*/I)_VweightGF)-F#6$I'sparseGF)F,/I+_EdgeIndexGF)-F#6 $I*symmetricGF)7+/6$F9F:<$I#e9GF)I$e10GF)/6$F4F8<#I#e7GF)/6$F4F5<#I#e3 GF)/6$F4F9<#I#e8GF)/6$F3F4<#I#e2GF)/6$F6F7<#I#e5GF)/6$F2F3<#I#e1GF)/6$ F7F8<#I#e6GF)/6$F5F6<#I#e4GF)/I/_EconnectivityGF)Ffo/I*_EmaxnameGF)\"# 5/I&_HeadGF)F*/I)_EweightGF)-F#6#7,/FdoF2/FIF2/FNF2/F\\oF2/FhnF2/F`oF2 /FJF2/FZF2/FVF2/FRF2/I'_EdgesGF)<,F\\oFZFRFdoFhnF`oFNFVFIFJ/I+_Neighbo rsGF)-F#6#7+/F2<#F3/F3<$F2F4/F4<&F3F5F8F9/F6<$F5F7/F5<$F4F6/F8<$F4F7/F 7<$F6F8/F9<$F4F:/F:<#F9/I(_StatusGF)<#I+MULTIGRAPHGF)/I&_EndsGF)-F#6#7 ,/Fdo<$F5F6/FI<$F9F:/FN<$F4F8/F\\o<$F2F3/Fhn<$F6F7/F`o<$F7F8/FJFas/FZ< $F3F4/FV<$F4F9/FR<$F4F5/I._BicomponentsGF)Fbt/I+_CountcutsGF)Fdt" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "G:=void(5):addedge(Cycle(1,2 ,3,4,5),G);draw(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'I#e1G6\"I#e2GF$ I#e3GF$I#e4GF$I#e5GF$" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6.-%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\" \"\"!$F-F--F(6#7$$\"+Q*p,4$!#5$\"+l^c5&*F4-F(6#7$$!+]*p,4)F4$\"+9D&y(e F4-F(6#7$$!+M*p,4)F4$!+PD&y(eF4-F(6#7$$\"+l*p,4$F4$!+c^c5&*F4-%%TEXTG6 $7$$\"2-++++++?\"!#;$F-!\"\"Q\"16\"-FM6$7$$\"+Q*p,4&F4F5Q\"2FV-FM6$7$$ !+&*p,45!\"*$\"1-++9D&y(eFRQ\"3FV-FM6$7$$!2-++I*p,45FRFCQ\"4FV-FM6$7$$ \"1+++l*p,4&FRFJQ\"5FV-%'CURVESG6(7$F*F17$F*FG7$F1F97$F9F@7$F@FG-%&COL ORG62%$RGBGFS$\"#5FTFSFSFhpFSFSFhpFSFSFhpFSFSFhpFS" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve \+ 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" }} {TEXT 208 0 "" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 37 "7.1.20. \303\201ll\303\255t\303 \241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 37 "7.1.21. \303\201ll\303\255t\303\241s." } }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.22. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.23. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 50 "7.1.24. \303\226sszef\303\274gg\305\221s\303\251g." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "G:= random(12,6):ends(G);components(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "< (<$\"\"#\"\"$<$\"\"'\"\")<$F%F(<$\"\"%F'<$F$\"#5<$F$\"#7" }}{PARA 11 " " 1 "" {XPPMATH 20 "<(<#\"\"\"<#\"\"&<#\"\"(<#\"\"*<#\"#6<)\"\"#\"\"$ \"\"%\"\"'\"\")\"#5\"#7" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%# %?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.25. Feladat." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.26. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.1.27. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 19 "7.1.28. F\303\241k." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "7.1. 29. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "7.1.30. T\303\251tel." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "7.1.31. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7. 1.32. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.33. Fel adat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 16 "7.1.34. Feladat." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.1.35. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 32 "7.1.36. Fesz\303\255t\305\221fa." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "G51:=cycle(4):dra w(G51);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6/-%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--% %TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q\"16\"-F(6#7$$!+3Q.^?!#>F+-F(6#7$$ F7F-$!+:w1-TF?-F(6#7$$\"+A95`hF?FC-%'CURVESG6$7$F*F<-%&COLORG6&%$RGBGF 6$\"#5F7F6-FL6$7$F " 0 "" {MPLTEXT 1 0 51 "G52:=void(4):addedge(Cycle(1,2,4,3),G52);draw(G52) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&I#e1G6\"I#e2GF$I#e3GF$I#e4GF$" }} {PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6/ -%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2- ++++++?\"!#;$F-!\"\"Q\"16\"-F(6#7$$!+3Q.^?!#>F+-F(6#7$$F7F-$!+:w1-TF?- F(6#7$$\"+A95`hF?FC-%'CURVESG6$7$F*F<-%&COLORG6&%$RGBGF6$\"#5F7F6-FL6$ 7$F " 0 "" {MPLTEXT 1 0 39 "spantree(G52):edges(%);counttrees(G52);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I#e1G6\"I#e2GF$I#e4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 37 "7.1.37. \303\201ll\303\255t\303\241s." } }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 37 "7.1.38. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 26 "7.1.39. Megjegyz\303\251s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "G6:=tetrahedron():sho w(G);cyclebase(G6);draw(G6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLE G%*protectedG6#70/I&_TailG6\"-F#6#7\"/I,_CounttreesGF)F./I*_VerticesGF )<.\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7/I)_Vweig htGF)-F#6$I'sparseGF)F,/I+_EdgeIndexGF)-F#6$I*symmetricGF)7(/6$F7F9<#I #e2GF)/6$F5F7<#I#e4GF)/6$F4F9<#I#e3GF)/6$F3F4<#I#e1GF)/6$F3F=<#I#e6GF) /6$F3F;<#I#e5GF)/I/_EconnectivityGF)F\\o/I*_EmaxnameGF)F7/I&_HeadGF)F* /I)_EweightGF)-F#6#7(/FPF2/FXF2/FjnF2/FfnF2/FLF2/FTF2/I'_EdgesGF)<(FXF LFTFPFjnFfn/I+_NeighborsGF)-F#6#7./F2<\"/F3<%F4F;F=/F4<$F3F9/F6Fep/F5< #F7/F8Fep/F7<$F5F9/F;<#F3/FF+-F(6#7$$F7F-$!+:w1-TF?-F(6#7$$\"+A95`hF ?FC-%'CURVESG6)7$F*F<7$F " 0 "" {MPLTEXT 1 0 22 "cycle(4):countcu ts(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "7 .1.42. Erd\305\221." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.43. Feladat." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "7.1.44. Euler-vonal." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 37 "7.1.45. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.46. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1 .47. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 27 "7.1.48. Hamilt on-\303\272t." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.49. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.50. Feladat." }}}{SECT 1 {PARA 5 " " 0 "" {TEXT 207 16 "7.1.51. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7. 1.52. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.53. Fel adat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.1.54. Feladat." }} }{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.1.55. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.1.56. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.1.57. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 25 "*7.1.58. Feladat: Dirac t" }{TEXT 207 8 "\303\251" }{TEXT 207 5 "tele." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.1.59. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 9 "7.1.60. C" }{TEXT 207 8 "\303 \255" }{TEXT 207 2 "mk" }{TEXT 207 8 "\303\251" }{TEXT 207 5 "zett " } {TEXT 207 41 "\303\251s s\303\272lyozott gr\303\241fok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "new(G 9):addvertex([v1,v2,v3,v4],weights=[2,4,6,8],G9);addedge([\{v1,v2\},\{ v2,v3\},\{v1,v3\},\{v3,v4\}],weights=[1,1,1,3],G9);show(G9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&I#v1G6\"I#v2GF$I#v3GF$I#v4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&I#e1G6\"I#e2GF$I#e3GF$I#e4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6#70/I&_TailG6\"-F#6#7\"/I,_Counttr eesGF)F./I*_VerticesGF)<&I#v1GF)I#v2GF)I#v3GF)I#v4GF)/I)_VweightGF)-F# 6$I'sparseGF)7&/F5\"\")/F3\"\"%/F4\"\"'/F2\"\"#/I+_EdgeIndexGF)-F#6$I* symmetricGF)7&/6$F4F5<#I#e4GF)/6$F3F4<#I#e2GF)/6$F2F3<#I#e1GF)/6$F2F4< #I#e3GF)/I/_EconnectivityGF)Fen/I*_EmaxnameGF)F?/I&_HeadGF)F*/I)_Eweig htGF)-F#6#7&/FM\"\"$/FU\"\"\"/FQFbo/FYFbo/I'_EdgesGF)<&FUFQFYFM/I+_Nei ghborsGF)-F#6#7&/F5<#F4/F3<$F2F4/F4<%F2F3F5/F2<$F3F4/I&_EndsGF)-F#6#7& /FM<$F4F5/FU<$F2F3/FQFdp/FYF`p/I._BicomponentsGF)Faq/I+_CountcutsGF)Fc q" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 11 "7.1.61. Moh" }{TEXT 207 8 "\303\263" }{TEXT 207 17 " algoritmus minim" }{TEXT 207 8 "\303\241" }{TEXT 207 4 "lis " }{TEXT 207 8 "\303\266" }{TEXT 207 4 "sszs" } {TEXT 207 8 "\303\272" }{TEXT 207 2 "ly" }{TEXT 207 8 "\303\272" } {TEXT 207 5 " fesz" }{TEXT 207 8 "\303\255" }{TEXT 207 1 "t" }{TEXT 207 8 "\305\221" }{TEXT 207 3 "erd" }{TEXT 207 8 "\305\221" }{TEXT 207 11 " konstrukci" }{TEXT 207 8 "\303\263" }{TEXT 207 1 "j" }{TEXT 207 8 "\303\241" }{TEXT 207 3 "ra." }}{PARA 0 "" 0 "" {TEXT 201 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "spantree(G9):ends(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "<%<$I#v1G6\"I#v2GF%<$I#v3GF%I#v4GF%<$F$F (" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 11 "7.1.62. Moh" }{TEXT 207 8 "\303\263" } {TEXT 207 14 " algoritmusok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 22 "7.1.63. Feladat: mi nim" }{TEXT 207 8 "\303\241" }{TEXT 207 4 "lis " }{TEXT 207 8 "\303\26 6" }{TEXT 207 4 "sszs" }{TEXT 207 8 "\303\272" }{TEXT 207 2 "ly" } {TEXT 207 8 "\303\272" }{TEXT 207 5 " fesz" }{TEXT 207 8 "\303\255" } {TEXT 207 1 "t" }{TEXT 207 22 "\305\221fa fan\303\266" }{TEXT 207 5 "v eszt" }{TEXT 207 8 "\303\251" }{TEXT 207 5 "ssel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 24 "7.1.64. Feladat: piros-k" }{TEXT 207 8 "\303\251" }{TEXT 207 13 "k algoritmus." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "*7.1.65. Feladat: a k" }{TEXT 207 8 "\303\255" }{TEXT 207 8 "nai post" }{TEXT 207 8 "\303\241" } {TEXT 207 7 "s-probl" }{TEXT 207 8 "\303\251" }{TEXT 207 3 "ma." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 25 "*7.1.66. Feladat: az utaz" } {TEXT 207 8 "\303\263" }{TEXT 207 2 " " }{TEXT 207 8 "\303\274" } {TEXT 207 3 "gyn" }{TEXT 207 8 "\303\266" }{TEXT 207 7 "k probl" } {TEXT 207 8 "\303\251" }{TEXT 207 1 "m" }{TEXT 207 8 "\303\241" }{TEXT 207 3 "ja." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 11 "7.1.67. Tov" } {TEXT 207 8 "\303\241" }{TEXT 207 14 "bbi feladatok." }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 43 "7.2. Ir\303\241ny\303\255tott gr\303\241 fok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 46 "7.2.1. Ir\303\241ny\303\255tott gr\303\241fok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart ;with(networks);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7hoI)acycpolyG6\"I(a ddedgeGF$I*addvertexGF$I*adjacencyGF$I)allpairsGF$I)ancestorGF$I)arriv alsGF$I-bicomponentsGF$I)charpolyGF$I*chrompolyGF$I+complementGF$I)com pleteGF$I+componentsGF$I(connectGF$I-connectivityGF$I)contractGF$I*cou ntcutsGF$I+counttreesGF$I%cubeGF$I&cycleGF$I*cyclebaseGF$I)daughterGF$ I*degreeseqGF$I'deleteGF$I+departuresGF$I)diameterGF$I&dinicGF$I+djspa ntreeGF$I-dodecahedronGF$I%drawGF$I'draw3dGF$I*duplicateGF$I&edgesGF$I %endsGF$I(eweightGF$I%flowGF$I)flowpolyGF$I(fundcycGF$I)getlabelGF$I&g irthGF$I&graphGF$I*graphicalGF$I&gsimpGF$I'gunionGF$I%headGF$I,icosahe dronGF$I*incidenceGF$I)incidentGF$I)indegreeGF$I'induceGF$I)isplanarGF $I*maxdegreeGF$I'mincutGF$I*mindegreeGF$I*neighborsGF$I$newGF$I+octahe dronGF$I*outdegreeGF$I%pathGF$I)petersenGF$I'randomGF$I%rankGF$I)rankp olyGF$I.shortpathtreeGF$I%showGF$I'shrinkGF$I%spanGF$I)spanpolyGF$I)sp antreeGF$I%tailGF$I,tetrahedronGF$I*tuttepolyGF$I(vdegreeGF$I)vertices GF$I%voidGF$I(vweightGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "G:=void(6):addedge([[1,2],[2,4],[1,3],[3,6],[2,6],[1,5]],G);\n" } {MPLTEXT 1 0 22 "tail(e1,G);head(e1,G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(I#e1G6\"I#e2GF$I#e3GF$I#e4GF$I#e5GF$I#e6GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "indegree(2,G);outdegree(2,G);" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "addedge([1,2],G);t ail(%,G);head(%%,G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#e7G6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "show(G);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&TABLEG%*protectedG6#71/I._BicomponentsG6\"F (/I)_VweightGF)-F#6$I'sparseGF)7\"/I&_EndsGF)-F#6#7)/I#e3GF)<$\"\"\"\" \"$/I#e6GF)<$F8\"\"&/I#e2GF)<$\"\"#\"\"%/I#e5GF)<$FA\"\"'/I#e4GF)<$F9F F/I#e1GF)<$F8FA/I#e7GF)FL/I&_TailGF)-F#6#7)/F6F8/F;F8/F?FA/FDFA/FHF9/F KF8/FNF8/I/_EconnectivityGF)Ffn/I*_VerticesGF)<(F8FAF9FBF=FF/I+_EdgeIn dexGF)-F#6$I*symmetricGF)7(/6$FAFF<#FD/6$F9FF<#FH/6$F8FA<$FKFN/6$F8F=< #F;/6$F8F9<#F6/6$FAFB<#F?/I+_CountcutsGF)Fcp/I,_CounttreesGF)Fep/I&_He adGF)-F#6#7)/F6F9/F;F=/F?FB/FDFF/FHFF/FKFA/FNFA/I+_NeighborsGF)-F#6#7( /F8<%FAF9F=/FA<%F8FBFF/F9<$F8FF/F=<#F8/FB<#FA/FF<$FAF9/I(_StatusGF)<$I +MULTIGRAPHGF)I)DIRECTEDGF)/I*_EmaxnameGF)\"\"(/I)_EweightGF)-F#6#7)FT FU/F?F8/FDF8/FHF8FYFZ/I'_EdgesGF)<)FKF?F6FHFDF;FN" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 20 "7.2.2. P\303\251lda." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "->7. 2.3. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "->7.2.4. Felad at." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "->7.2.5. Feladat." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.2.6. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.2.7. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "7.2.8. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 65 "7.2.9. Ir\303\241ny\303\255tott gr\303\241fok izomorfi\303\241 ja." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 9 "7.2.10. P" }{TEXT 207 20 "\303\251ld\303 \241k." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 9 "7.2.11. V" }{TEXT 207 34 "\303\251ges gr \303\241fok \303\251" }{TEXT 207 5 "llist" }{TEXT 207 8 "\303\241" } {TEXT 207 2 "s " }{TEXT 207 8 "\303\241" }{TEXT 207 2 "br" }{TEXT 207 8 "\303\241" }{TEXT 207 3 "zol" }{TEXT 207 8 "\303\241" }{TEXT 207 3 " sa." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 56 "7.2.12. Ir\303\241ny\303\255tott r\303\2 51szgr\303\241f." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT 207 98 "7.2.13. Ir\303\241ny\303\255tot t s\303\251t\303\241k, vonalak, utak \303\251s k\303\266r\303\266k." } }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 27 "*7.2.14. Topologikus rendez" }{TEXT 207 8 "\303\25 1" }{TEXT 207 2 "s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 62 "7.2.15. Er\305\221s \303\266 sszef\303\274gg\305\221s\303\251g." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 36 "7.2.16. Ir\30 3\241ny\303\255tott fa." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 9 "7.2.17. K" }{TEXT 207 8 "\303\266" }{TEXT 207 10 "nig-lemma." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 16 "*7.2.18. Kupac. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 20 "*7.2.19. Kupacrendez" }{TEXT 207 8 "\30 3\251" }{TEXT 207 3 "s. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%# %?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 15 "*7.2.20. B-fa. " }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "*7.2.21. Oszd meg " }{TEXT 207 8 "\303\251" }{TEXT 207 12 "s uralkodj. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 27 "*7.2.22. Dijksra modszere. \+ " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.23. Megjegyz" }{TEXT 207 8 "\303\251" } {TEXT 207 3 "s. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT 207 28 "*7.2.24. Dinamikus programoz" } {TEXT 207 8 "\303\241" }{TEXT 207 3 "s. " }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.25. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.26. Feladat ." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.27. Feladat." }}} {SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.28. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 11 "*7.2.29. Sz" }{TEXT 207 8 "\303\251" }{TEXT 207 4 "less" }{TEXT 207 8 "\303\251" }{TEXT 207 6 "gi bej" }{TEXT 207 8 "\303\241" }{TEXT 207 1 "r" }{TEXT 207 8 "\303\241" }{TEXT 207 2 "s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 10 "*7.2.30. M" }{TEXT 207 8 "\303\251" }{TEXT 207 3 "lys" } {TEXT 207 8 "\303\251" }{TEXT 207 6 "gi bej" }{TEXT 207 8 "\303\241" } {TEXT 207 1 "r" }{TEXT 207 8 "\303\241" }{TEXT 207 2 "s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 44 "*7.2.31. Feladat: Warshall-Floyd-algoritmus." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.32. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 19 "*7.2.33. Feladat : e" }{TEXT 207 28 "r\305\221s komponensek megha" }{TEXT 207 1 "t" } {TEXT 207 8 "\303\241" }{TEXT 207 3 "roz" }{TEXT 207 8 "\303\241" } {TEXT 207 3 "sa." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 0 {PARA 5 "" 0 "" {TEXT 207 14 "*7.2.34. PERT." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.35. Feladat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "% #%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 20 "*7.2.36. Folyamprobl" }{TEXT 207 8 "\303\251" }{TEXT 207 3 "ma." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 15 "*7.2.37. Lemma." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT 207 25 "*7.2.38. Ford-Fulkerson-t" } {TEXT 207 8 "\303\251" }{TEXT 207 10 "tel (maxim" }{TEXT 207 8 "\303\2 41" }{TEXT 207 17 "lis folyam, minim" }{TEXT 207 8 "\303\241" }{TEXT 207 5 "lis v" }{TEXT 207 8 "\303\241" }{TEXT 207 1 "g" }{TEXT 207 8 " \303\241" }{TEXT 207 3 "s t" }{TEXT 207 8 "\303\251" }{TEXT 207 5 "tel )." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 34 "*7.2.39. Edmonds-Karp-heu risztika." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 16 "*7.2.40. Dinic m" }{TEXT 207 8 "\303\263" }{TEXT 207 7 "dszere." }}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7 .2.41. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.42. Fel adat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "*7.2.43. Feladat: " } {TEXT 207 8 "\303\241" }{TEXT 207 4 "ltal" }{TEXT 207 8 "\303\241" } {TEXT 207 3 "nos" }{TEXT 207 8 "\303\255" }{TEXT 207 16 "tott folyampr obl" }{TEXT 207 8 "\303\251" }{TEXT 207 3 "ma." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 26 "*7.2.44. Feladat: Menger t" }{TEXT 207 24 "\303\251 tele elv\303\241" }{TEXT 207 1 "g" }{TEXT 207 8 "\303\263" }{TEXT 207 1 " " }{TEXT 207 8 "\303\251" }{TEXT 207 10 "lhalmazra." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 26 "*7.2.45. Feladat: Menger t" }{TEXT 207 24 "\303\251tele elv\303\241" }{TEXT 207 1 "g" }{TEXT 207 8 "\303\263" }{TEXT 207 3 " cs" }{TEXT 207 8 "\303\272" }{TEXT 207 11 "cshalmazra. " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 19 "*7.2.46. Feladat: K" }{TEXT 207 8 "\303\266" }{TEXT 207 5 "nig t" }{TEXT 207 8 "\303\251" }{TEXT 207 5 "tele." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 52 "*7.2.47. Gr\303 \241fok rajzolhat\303\263s\303\241ga." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 38 "*7.2 .48. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 34 "*7.2.49. Seg \303\251dt\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%? G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 22 "*7.2.50. T\303\251tel." } }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.2.51. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.2.52. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 28 "*7.2.53. Tartom\303\241nyok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 29 "*7.2 .54. Euler t\303\251tele." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "% #%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 27 "*7.2.55. Megjegyz\303 \251s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 11 "*7.2.56. Gr" }{TEXT 207 8 "\303\241" } {TEXT 207 30 "fok topologikus izomorfizmusa." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 34 "*7.2.57. Kuratowski t\303\251tele." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "G:=tetrahe dron():draw(G);isplanar(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" } {GLPLOT2D 400 400 400 {PLOTDATA 2 "6,-%*AXESSTYLEG6#%%NONEG-%'POINTSG6 #7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q\"16\"-F(6#7 $$!+3Q.^?!#>F+-F06$7$$!+-+++?!#5$\"#5F7Q\"2F9-F(6#7$$F7F-$!+:w1-TF?-F0 6$7$$!2-++++++?\"F5$!%-T!#8Q\"3F9-F(6#7$$\"+A95`hF?FL-F06$7$$\"+1+++?F E$FEF7Q\"4F9-%'CURVESG6)7$F*F<7$F*FK7$F*FZ7$F " 0 "" {MPLTEXT 1 0 37 "G:=icosahedron():draw(G);isplanar(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6=-%*AXESSTYLE G6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--F(6#7$$!+3Q.^?!#>F+-%'CURVES G6$7$F*F1-%&COLORG6&%$RGBG$F-!\"\"$\"#5F>F=-%%TEXTG6$7$$\"2-++++++?\"! #;F=Q\"06\"-F(6#7$$\"+PSDg')!#5$\"+-+++]FO-FB6$7$$\"2-++SSDg1\"FGFPQ\" 1FI-F(6#7$$\"+$*******\\FO$\"+USDg')FO-FB6$7$$\"+$*******pFOFgnQ\"2FI- FB6$7$$!+-+++?FOF?Q\"3FI-F(6#7$$!+0+++]FO$\"+NSDg')FO-FB6$7$$!+0+++qFO FjoQ\"4FI-F(6#7$$!+VSDg')FO$\"+\"*******\\FO-FB6$7$$!2-++SSDg1\"FGFgpQ \"5FI-F(6#7$$F>F-$!+in?59!#=-FB6$7$$!2-++++++?\"FG$!,?w1-T\"F4Q\"6FI-F (6#7$$!+HSDg')FO$!+;+++]FO-FB6$7$$!+.a-m5!\"*FcrQ\"7FI-F(6#7$$!+*)**** **\\FO$!+WSDg')FO-FB6$7$$!+*)******pFOFasQ\"8FI-F(6#7$$\"+U,J:;FeqFbq- FB6$7$$\"+;+++?FO$FOF>Q\"9FI-F(6#7$$\"+<+++]FO$!+GSDg')FO-FB6$7$$\"+<+ ++qFO$!1+++GSDg')FGQ#10FI-F(6#7$$\"+]SDg')FO$!+z******\\FO-FB6$7$$\"+0 a-m5FjrFiuQ#11FI-F66@7$F*FL7$F*FZ7$F*Fgo7$F*F`r7$FLFZ7$FLFgo7$FLFdp7$F LF^s7$FZF17$FZFdp7$FZFaq7$F1Faq7$F1F`r7$F1F[t7$FgoF`r7$FgoF^s7$FgoFgt7 $FdpFaq7$FdpF^s7$FdpFfu7$FaqF[t7$FaqFfu7$F`rF[t7$F`rFgt7$F^sFgt7$F^sFf u7$F[tFgt7$F[tFfu7$FgtFfu-F:6dpF " 0 "" {MPLTEXT 1 0 35 "G:=complete(5):draw(G);isplanar(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6.-%*AXESSTYLEG6 #%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F -!\"\"Q\"16\"-F(6#7$$\"+Q*p,4$!#5$\"+l^c5&*F?-F06$7$$\"+Q*p,4&F?F@Q\"2 F9-F(6#7$$!+]*p,4)F?$\"+9D&y(eF?-F06$7$$!+&*p,45!\"*$\"1-++9D&y(eF5Q\" 3F9-F(6#7$$!+M*p,4)F?$!+PD&y(eF?-F06$7$$!2-++I*p,45F5FgnQ\"4F9-F(6#7$$ \"+l*p,4$F?$!+c^c5&*F?-F06$7$$\"1+++l*p,4&F5FdoQ\"5F9-%'CURVESG6-7$F*F <7$F*FJ7$F*FZ7$F*Fao7$F " 0 "" {MPLTEXT 1 0 37 "G:=complete(3,3):draw(G);isplanar(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "60-%*AXESSTYLEG6#%%NONEG-%'PO INTSG6#7$$\"\"\"\"\"!$F-F--%%TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q\"16\" -F(6#7$$\"+-+++]!#5$\"+PSDg')F?-F06$7$$\"+-+++qF?F@Q\"2F9-F(6#7$$!+(** *****\\F?$\"+SSDg')F?-F06$7$$!+(*******pF?$\"*/a-m)!\"*Q\"3F9-F(6#7$$F 7F-$\"+&QKz*e!#>-F06$7$$!2-++++++?\"F5$\"1-++&QKz*e!#DQ\"4F9-F(6#7$$!+ 2+++]F?$!+MSDg')F?-F06$7$$!+2+++qF?FgoQ\"5F9-F(6#7$$\"+\"*******\\F?$! +VSDg')F?-F06$7$$\"+\"*******pF?$!1+++VSDg')F5Q\"6F9-%'CURVESG6,7$F*FZ 7$F*Fdo7$F*Fap7$F%$RGB GF6$\"#5F7F6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6F6F^rF6" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10 " "Curve 11" "Curve 12" "Curve 13" }}{TEXT 208 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "G:=petersen():draw(G);isplanar(G);" }}{PARA 13 "" 1 " " {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6;-%*AXESSTYLEG6# %%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--F(6#7$$\"+Q*p,4$!#5$\"+l^c5&*F4 -F(6#7$$!+]*p,4)F4$\"+9D&y(eF4-F(6#7$$!+M*p,4)F4$!+PD&y(eF4-F(6#7$$\"+ l*p,4$F4$!+c^c5&*F4-%'CURVESG6$7$F*F9-%&COLORG6&%$RGBG$F-!\"\"$\"#5FUF T-FM6$7$F*F@FP-FM6$7$F1FGFP-%%TEXTG6$7$$\"2-++++++?\"!#;FTQ\"66\"-Fin6 $7$$\"+Q*p,4&F4F5Q\"8F`o-Fin6$7$$!+&*p,45!\"*$\"1-++9D&y(eF^oQ#10F`o-F in6$7$$!2-++I*p,45F^oFCQ\"7F`o-Fin6$7$$\"1+++l*p,4&F^oFJQ\"9F`o-F(6#7$ $\"+nmmm;F\\pF.-Fin6$7$$\"+nmmm=F\\pFTQ\"1F`o-F(6#7$$\"+IKG]^F4$\"+%>% 4&e\"F\\p-Fin6$7$$\"1-++IKG]rF^oF\\rQ\"2F`o-F(6#7$$!+e;O[8F\\p$\"+d3U' z*F4-Fin6$7$$!2-++!e;O[:F^oFirQ\"3F`o-F(6#7$$!+c;O[8F\\p$!+&*3U'z*F4-F in6$7$$!2-++glh$[:F^o$!1+++&*3U'z*F^oQ\"4F`o-F(6#7$$\"+vKG]^F4$!+$>%4& e\"F\\p-Fin6$7$$\"+vKG]rF4$!2-++I>%4&e\"F^oQ\"5F`o-FM6/7$F^qFiq7$FiqFf r7$FfrFcs7$FcsFbt7$F^qFbt7$F@F17$FGF97$FcsF@7$F^qF*7$FiqF17$FfrF97$Fbt FG-FQ6GFSFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTFTFVFTF TFVFTFTFVFT" 1 2 2 1 10 1 2 6 1 1 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Cur ve 22" "Curve 23" "Curve 24" }}{TEXT 208 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.58. Fela dat." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.59. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.60. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.61. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 17 "*7.2.62. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 21 "7.2.63 . Kromatikus sz" }{TEXT 207 8 "\303\241" }{TEXT 207 2 "m." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 18 "->7.2.64. Feladat." }}}{SECT 1 {PARA 5 " " 0 "" {TEXT 207 16 "7.2.65. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.2.66. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.2.67. Feladat." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 207 16 "7.2.68. Feladat." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 207 38 "7.2.69. Gr\303\241 fok m\303\241trixai." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "G:=tetrahedron():draw(G);adjacency(G);inc idence(G);" }}{PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6,-%*AXESSTYLEG6#%%NONEG-%'POINTSG6#7$$\"\"\"\"\"!$F-F--% %TEXTG6$7$$\"2-++++++?\"!#;$F-!\"\"Q\"16\"-F(6#7$$!+3Q.^?!#>F+-F06$7$$ !+-+++?!#5$\"#5F7Q\"2F9-F(6#7$$F7F-$!+:w1-TF?-F06$7$$!2-++++++?\"F5$!% -T!#8Q\"3F9-F(6#7$$\"+A95`hF?FL-F06$7$$\"+1+++?FE$FEF7Q\"4F9-%'CURVESG 6)7$F*F<7$F*FK7$F*FZ7$F " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }