图的子图中(n,r)-正交因子分解

设图G的顶点集为V(G)，边集为E(G)，g和f是定义在V(G)上的2个整值函数，满足对于一切x∈V(G)，g(x)≤f(x).若G是一个(mg+rn，mf-rn)-图，1≤n＜m，r≥2，且对于x∈V(G)，有g(x)≥k≥1，则存在G的一个子图G′，使得G′具有一个(f，g)-因子(n，r)-正交于G的任意给定子图H，其中｜E(H)｜=nk.

(n,r)-Orthogonal Factorizations in Subgraphs of Graphs

Let G be a graph with vertex set V(G) and edge set E(G),and let g and f be two integer - valuedfunctions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G).It is proved that if G is an (mg + m,mf- rn) - graph,1 ≤ n ＜ m,r ≥ 2,and g(x) ≥ k ≥ 1 for all x ∈ V(G), then there exists a subgraph G'of Gsuch that G' has a (g,f) - factorization (n, r ) - orthogonal to any given subgraph H of G with |E(H)|= nk.