Stability Number and Fractional F-factors in Graphs

摘要

Let G be a graph with vertex set V(G) and let / be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional /-factor if cIq(x) = f(x) for every x G V(F). In this paper we prove that if S(G) > b, and a(G) < 4,°^~,y, then G has a fractional f-factor. Where a and b are integers such that 0 < a < fix) S: b f°r every x ? V(G). Therefore we prove that the fractional analogue of Conjecture in [2] is true.