图中子图的正交(g,f)-因子分解

Orthogonal (g, f )-factorizations in subgraphs of graphs

设g和f是两个定义在图G顶点集上的整值函数,使得对G的所有顶点x有g(x)≤f(x)。证明了以下结果:如果G是一个(mg+r,mf-r)-图,1≤r<m,并对G的所有顶点x有g(x)≥k≥1,则存在G的一个子图H,使得H有一个(g,f)-因子分解与G的给定的k个具有r+1条边且点不相交的子图正交.PBCLam发表的结果是这一结论的特殊情形。参10。

Let g and f be two integer-valued functions defined on vertex set of G such that g(x)≤f(x) for each vertex x of G. It is proved that if G is an (mg + r, mf - r)-graph, 1≤r <m, and g(x) ≥ k ≥1 for each vertex x of G,then there exists a subgraph H of G such that H has a (g,f)-factorization orthogonal to k subgraphs of G, which are given vertex-disjoint subgraphs with r+1 edges. The P B C. Lam's result published is a special case of this result. 10refs.