25579.圖的2距離染色

1、圖的2一距離染色2DistanceColoringofGraphs作者嚴(yán)曉燕Author：№圣i型塑指導(dǎo)教師：卜月華Supervisor：專(zhuān)業(yè)：運(yùn)籌學(xué)與控制論Major：學(xué)B玎翰ehuaOperationalResearchandCybernetics位：理學(xué)碩士Degree：叢墾璺主竺Q!墨璺i旦翌堡授予單位：浙江師范大學(xué)Institute：——ZhejiangNormalUniversity——March，20142Distance

2、ColoringofGraphsABSTRACTAllgraphsconsideredinthispaperarefinitesimplegraphs；the2distance七一coloringofagraphGisamappingC：v(c)一1，2，，七)suchthatc(u)≠c(v)foreverypairofverticesUandVsatisfying0dG(U，口)≤2Wedefinex2(G)=minkGadmits

3、a2distancekcoloringasthe2distancechromaticnumberofagraphGAlistassignmentofagraphGisamappingLwhichassignstoeachvertexVasetL(v)ofpositiveintegersWesayGis2distanceL—colorableifthereexistsapropervertexcoloringCofGsuchthatc(v

4、)∈L(v)foreveryV∈y(G)AgraphGislist2distancekcolorableifGis2distanceL—colorableforeverylistassignmentLwithIL(u)I=kforallV∈y(G)Wedefine)(!(G)=rainkGadmitsalist2distancekcoloringasthelist2distancechromaticnumberofagraphGAbou

5、tthe2distancecoloringofplanargraphs，in1977，Wegnerposedthefollow—ingconjecture：foraplanargraphG，ifA(c)=3，thenx2(G)≤7；if4≤A(c)≤7，thenx2(G)≤A(c)5；ifA(G)≥8，thenx2(c)≤12△(G)J1。Thispaperconsiststhreechaptersandmainlystudythe2d

6、istancecoloringofplanargraphswithoutspecialshortcyclesandgraphswithmaximumdegreenotmorethan5Inthefirstchapterweintroducesomebasicdefinitionsandtheresearchstatusof2distancecoloring，andgivestheresultsofthispaperInthesecond

7、chapter’wemainlystudythe2distancecoloringofplanargraphswithoutspecialshortcycles，provingthat(1)IfGisaplanargraphwithout3一，4一，8cyclesandwithA(c)≥14，then)(2(G)≤a(c)5(2)IfGisaplanargraphwithA(a)≥12whichcontainsno3一，5cyclesa