完全b-染色與b-邊染色的研究.pdf

1、大連海事大學碩士學位論文完全b染色與b邊染色的研究姓名：呂闖申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：王德強20100601英文摘要ABSTRACTTheproblemofcoloringandcoloringnumberaleaimportantcontentandaveryactivefieldofthegraphtheoryIthasveryprofoundandplentifultheoreticalresultandexten

2、sivepracticalapplicationThetheoryandmethodofcoloringindiscretemathematicsoccupiesanimportantpositionThebchromaticnumberofagraphWaSintroducedbyIrvingandManlovein1999Theyhaveshownthatdeterminationofb(G)isNPhardforgeneralgr

3、aphs，butpolynomialfortreeThebcontinuityofagraphwasintroducedbyFaikin2004HeprovethatthechordalgrapharebcontinuousThemainworksinthispaperasfollows：(1)Theproblemofbcoloringofthesquare鰣dgraphWasstudied，thebchromaticnumberofi

4、twasgiven，anditisprovedthatthesquare鰣dgraphisbcontinuous(2)theconceptofthecompletebchromaticnumberandthecompletebcontinuityofagraphisproposed，andthecompletebchromaticnumberofpath，circle，squaregridandfully11arytreegraphsa

5、restudied，anditisproventhatallthesegraphsareb—continuousinthepaper(3)Theconceptofthebedgechromaticnumberandthebedgecontinuityofagraphisproposed，andthebedgechromaticnumberofpath，circle，squaregridandfullyn—arytreegraphsale

6、given，anditisproventhatpath，circleandfullyn—arytreegraphsarebedgecontinuousinthepaper(4)Theconceptofthecompletebedgechromaticnumberandthecompletebedgecontinuityofagraphisproposed，andthecompletebedgechromaticnumberofpath，

7、circleandfullyn—arytreegraphsaregiven，anditisproventhatallthesegraphsarecompletebedgecontinuousinthepaperKeyWords：bchromaticnumber；bcontinuity；completebchromaticnumerber；completebeontinuity；bedgechromaticnumber；bedgecont