18715.若干圖的邊染色和全染色

1、若干圖的邊染色和全染色Edgecoloringandtotalcoloringofsomegraphs作者：楊燦權(quán)指導教師：王維凡專業(yè)：墼堂Major：學位：理學項士授予單位：浙江師范大學Degree：MathematicsMasterofScienceMay2015AbstractAproperkedgecoloringofGisamappingfromE(G)into1，2，，七]Isuchthatadjacentedgeshave

2、differentcolorsThechromaticindexx，(G)ofagraphGistheleast七suchthatGhasaproperkedgecoloringAproperktotalcoloringofGisamappingfromV(C)uE(G)into1，2，，南)suchthatnoincidentoradjacentelements(verticesoredges)receivethesamecolors

3、ThetotalchromaticnumberX，，(G)ofagraphGistheleastksuchthatGhasaproperktotalcoloringInthismasterthesis，westudytheedgecoloringandtotalcoloringofsomegraphS，includinggeneralizedMycielskigr印hs，cubicgraphs，1planegraphs，planegra

4、phsandoddgraphsWefocusonthePlanarEdgeColoringConjecture，ListEdgeColoringConjec—ture，TotalColoringConjectureandUniqueMaximumDegreeTotalColoringConjecture，andwewillgivesomeevidencestosupporttheseconjecturesThethesisconsist

5、softhreechaptersInChapter1，weintroducesomebasicnotation，giveachiefsurveyinthisdirectionandstatethemainresultsobtainedInChapter2，wefocusontheedgecoloringproblemofsomegr印hSandobtainthefollowingresults：(1)Characterisetheedg

6、echromaticnumberofgeneralizedMycielskigraphs；(2)Considerthefractionaledgechromaticnumberofplanargraphsandshowthatanycubicgrapllsare(7，2)一edgecolorable；(3)Studytheedgecoloringandlistedgecoloringof1planargraphsandplanargra

7、phsundertheconditionofthesubgraphinducedbythemaximumdegreeverticesInChapter3，wefocusonthetotalcoloringproblemofsomegraplls(1)ProvethatgeneralizedMycielskigraphsatisfiestheTotalColoringConjecture，andalsowegivesomesufficie

8、ntconditionsforagraphtobeType1；(2)Studythetotalcoloringandlisttotalcoloringof1planargraphsandplanargraphsundertheconditionofthesubgraphinducedbythemaximumdegreevertices；(3)ProvethatoddgraphssatisfytheTotalColoringConject