图的子图中 (n ,r) -正交因子分解(英文)

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

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 .

Let G be a graph with vertex set V(G) and edge set E(G) ,and let g and f be two integer-valued functions defined on V(G) such that g(x)≤f(x) for all x∈V(G) .It is proved that if G is an (mg+rn,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 G such that G′ has a (g,f) -factorization (n,r ) -orthogonal to any given subgraph H of G with | E(H)|=nk .