关键词: 简单图, 分数因子, 独立数, 最小度;分数一致图

Abstract: Let G be a graph with vertex set V(G), minimum degree  δ(G) and independent number α(G). Let k≥2 be an integer. A spanning subgraph F of G is called a fractional k-factor if dhG(x)=k for every x∈V(F). A graph G is called a fractional k-uniform graph if for each edge of G, there is a fractional k-factor containing it and another one excluding it. In this paper, we prove that if δ(G)≥k+2 and α(G)≤4k(δ-k-1)(k+1)2, then G is a fractional k-uniform graph.

Key words: simple graph, independent number, fractional factor, minimum degree, fractional uniform graph