关于图的(g,f)-因子分解的若干结果  

Some Results on (g, f)-Factorizations of Graphs

作　　者：李继猛[1] 李建湘[2] 杨喜陶[2] 

机构地区：[1]邵阳学院数学系,湖南邵阳422004 [2]湖南科技大学数学院,湖南湘潭411201

出　　处：《桂林工学院学报》2004年第4期512-515,共4页Journal of Guilin University of Technology

基　　金：~~

摘　　要：对目前关于图的因子分解研究中的3个问题进行了讨论,得到了以下结果:(1)设Z={x∈V(G):dG(x)-mg(x) t(x),或mf(x)-dG(x) t(x);t(x)=f(x)$Cg(x)>0}.当Z≠ 时,g和f可以不全为偶数,能使(mg,mf)-图有(g,f)-因子分解.(2)G是具有2n个顶点的m-正则图,m n.若(P1,P2,…,Pr)是m的一个划分,则G的边集E(G)能划分成r个部分E1,E2,…,Er,使G[Ei]是G的Pi-因子,其中Pi≡0(mod2),i=2,…,r;P1≡m(mod2).(3)G是具有2n个顶点的m-正则图,m n.若G不含有K3,则G有1-因子分解.Three problems for the study of factorizations of graphs are discussed.It is proved that:(1)Let Z= {x(V(G):d_(G)(x)-mg(x)t(x) or mf(x)-d_G(x) t(x);t(x) = f (x)-g(x)>0}.If Z≠,both g and f are not even,then(mg,mf)-graph has a (g,f)-factorization.(2)Let G be a m-regular graph with 2n vertices,mn.If (P_(1), P_(2),…, P_(r))is a partition of m, P_(1)≡m(mod 2),P_(i)≡0(mod 2),i = 2,…,r,then edge set E(G)of G can be parted into r parts E_(1), E_(2),…, E_(r)of E(G),so that G\ is P_(i)-factor of G.(3) Let G be a m-regular graph with 2n vertices,mn.If G contains no K_(3), G has 1-factorization.

关 键 词：图 因子 因子分解 

分 类 号：O157.5[理学—数学]