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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
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