Some Factorizations of Complete Bipartite Graphs.pdf

1、南開大學碩士學位論文SomeFactizationsofCompleteBipartiteGraphs姓名：孫霓剛申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：陳永川20040401SomeFactorizationsofCompleteBipartiteGraphs孫霓剛ABSTRACTLetⅣmnbeacompletebipartitegraphwithtwopartitesetshavingmandnverticesrespectiv

2、ely^Km，nisthemultigraphobtainedfromⅣⅢlbyreplacingeachedgeeof‰nbyasetof^edgesallhavingthesali]eendverticesaseAK1k一[actorofA‰nisaspanningsubgraphFofAKMsuchthateverycomponentofFisaKIkAⅣ1k一[actorizationofAⅣ叫isasetofedgedisjo

3、intKI，k一[actorsof^‰，nwhichpartitionthesetofedgesof^Km“Wecalltheuniquevertexwhichhasdegreekin耳l，≈astherootofK1≈I￡wedirecteachedgeofK1≈fromtheroottotheothervertex，thenwegetanorientationofKI，k，denotedbyK；kIfwereplaceeveryco

4、mponentofaKl≈一factorof^％，柚y耳；，≈，thenwegeta蜓＆factorofA‰m。AstheSall]e，wecandefineaⅣ；kfactorizationofA‰”InthispaperwefocusonsomespecialfactorizationsofA‰nFirst，wegiveanecessaryconditionfortheexistenceoftheK1，k—factorization

5、ofAKmn，where≈isanypositiveintegerSecond，whenA=1，P，，P。，wegiveasufficientconditionfortheK1Pc—factorizationofAKm，ntoexist，whereeisapositiveintegerandPis8primenumberAfterwardswediscusstheKI口。。factorizationof^‰㈣wherePandqmtwo

6、distinctprimenumbersAndwegiveasu幣cientconditionforsuchafactorizationtoexistinthecaseofA=】，n吼wFinaiiywefocusonakindofrestricted影j。蠡ctorizationsofK舢，wherePisaprimenumber。andgiveasumcientconditionforsuchafactorizationtoexis