【摘要】 设G是一个图,用V(G)和E(G)分别表示它的顶点集和边集,并设g(x)和f(x)分别是定义在V(G)上的非负整数值函数,且对每个x∈V(G)有g(x)<f(x),则图G的一个支撑子图F称为G的一个(g,f)-因子,如果对每个x∈V(G),有g(x)dF(x)f(x)。图G的(g,f)-因子分解是指E(G)能划分成边不交的(g,f)-因子,设F={F1,F2,…,Fm}和H分别是图G的因子分解和子图,若对所有1im有|E(H)∩E(Fi)|=r,则称F和H(m,r)-正交。文中定理1得到如下结果:若G是一个(mg+m-1,mf-(m-1)r)-图,H是G的一个有mr条边的子图,则G有一个(g,f)-因子分解与H(m,r)-正交。更多还原

【Abstract】 Let G be a graph with vertex set V(G) and edge set E(G),and Let g(x) and f(x) be two integer-valued functions defined on V(G) such as g(x) < f(x) for every x∈V(G).Then a(g,f)-factor of G is a spanning subgraph F of G such as g(x)≤dF(x)≤f(x) for every x∈V(G).The(g,f)-factorization of G is a partition of E(G) into edge-disjoint(g,f)-factors.Let F = { F1,F2,…,Fm} and H be the factorizations and a subgraph of G,respectively.If Fi,1≤i≤m has exactly r edges in common with H,then it is said that F is(m,r)-orthogonal to H.This paper proves that for any subgraph H with mr edges of an(mg + m-1,mf-(m-1) r)-graph G,there exists a(g,f) factorization(m,r)-orthogonal to H.更多还原