摘要
设G是一个 (mg +k ,mf -k) -图 (1≤k <m) ,g和 f分别是定义在图G的顶点集V(G)上的整数值函数且对每个x∈V(G)有 0≤g(x)≤f(x) ,H是G的任意一个有k条边的子图。文献 [2 ]提出了如下猜想 :设G是一个 (mg +k ,mf -k) -图 (1≤k <m) ,其中对任意的x∈V(G)有 0≤g(x)≤f(x)是定义在V(G)上的整数值函数 ,1≤k <m ,则G中存在子图R满足对G的任意子图H ,|E(H) | =k ,R有 (g ,f) -因子分解与H正交 ,并且文献 [2 ]证明了当 g(x)≥ 1,f(x)≥ 5时猜想成立 ,本文将证明对任意的 g 。
let G be a (mg+k,mf-k)-graph(1≤k<m),g and f be integer-valued functions defined on V(G) such that for each x∈V(G):0≤g(x)≤f(x).H is a subgraph of G with k edges.The conjecture in paper is:let G be a (mg+k,mf-k) =graph( 1≤k<m ),g and f be integer-valued functions defined on V(G) such that for each x∈V(G):0≤g(x)≤f(x) ,then there exists a subgraph R of G with ( g,f )-factorization orthogonal to H ,where H is a subgraph of G .Paper has proved tiat it is correct in the case of g(x)≥1,f(x)≥5 .In this paper,we will prove that the conjecture is correct for any g and f .
出处
《数学理论与应用》
2001年第3期35-39,共5页
Mathematical Theory and Applications
