图的边加权顶点着色.pdf

《图的边加权顶点着色.pdf》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、©aÒ:—?:UDC:?Ò:ÆØ©ã>º:XÚx•“6¶:M~“£Ǥàó’ŒÆžÆ?O:a¬Æ‰!;’¶¡:A^êÆØ©Jžm:2011c11Ø©‰Fžm:2011c12Æǃü:àó’ŒÆ‰F”¬ÌR:µ<:2011c12DissertationSubmittedtoHebeiUniversityofTechnologyforTheMasterDegreeofScienceinAppliedMathematicsVERTEX-COLORINGEDGE-WEIGHTINGSOFGRAPHSbyliYunyunSuper

2、visor:Prof.XuChangqingDec2011àó’ŒÆa¬ÆØ©ã>º:XÚÁ‡w´éãGk->D,w:E(G)!f1;2;


;kg.é?¿Pv2V(G),½ÂÙ>Ý•fw(v)=v2ew(e),K>DwŒ±ј‡º:XÚfw:V(G)!N.XJé?¿uv2E(G)Ñkfw(u)6=fw(v),K¡ãG#Nk->º:XÚ.ãGNNk->º:XÚ•k¡•ãG>º:XÚê,P•(G).©(½õÜãÚÜ©nÜãAÏã>º:XÚê.'…i:º:XÚ,>º:XÚ,õÜãiã>

3、º:XÚVERTEX-COLORINGEDGE-WEIGHTINGSOFGRAPHSABSTRACTAk-edge-weightingofgraphGisamappingw:E(G)!f1;2;


;kg.Anedge-weightingwinducesavertexcoloringfw:V(G)!N,wherePfw(v)=v2ew(e)foreachv2V(G).Furthermoreiffw(u)6=fw(v)foranyedgeuv2E(G),wesaythatGadmitsavertex-coloringk-edge-weighting.

4、TheminimumkforwhichGadmitsavertex-coloringk-edge-weightingisdenotedby(G).Theexactvaluesof(G)forsomeclassesofgraphs,includingcompletemultipartitegraph,sometripartitegraphsaredeterminedinthispaper.KEYWORDS:vertexcoloring,vertex-coloringedge-weighting,completemultipartitegraphiià

5、ó’ŒÆa¬ÆØ©8¹¥©Á‡........................................................................i=©Á‡........................................................................iiÎÒ`².......................................................................iv1˜ÙXØ..............................

6、.....................................1x11ãØuÐ........................................................1x12ãXÚ¯K......................................................2x13©¤ïÄSN.................................................41Ùã9XÚnØÄ•£..................................

7、.......5x21ãÄVg......................................................5x22>º:XÚÄ(Ø9ïÄyG..............................71nÙAaAÏã>º:XÚê...............................10x31(!÷!Ó>º:XÚê....................................10x32õÜã>º:XÚê..............................

8、.....12x33nÜã>º:XÚê........................