[a,b]-因子存在性的范-型条件

A Fan-Fype Condition for the Existence of [a,b]-Factors

设G是一个图,a,b是整数且满足0≤a≤b.如果存在G的一个支撑子图F,使对任意的x∈V(G)有a≤d_F(x)≤b,则称F是G的一个[a,b]-因子.本文给出图中具有特定性质的[a,b]-因子的范-型条件.进一步指出这个结果是最好的.

Let G be a graph, and let a,b be two integers with 0 ≤ a ≤ b. Then a spanning subgraph F of G is called an [a, b]-factor if a ≤ dF（x） ≤ b holds for each x ∈ V（G）. In this paper, we obtain a Fan-type condition for the existence of [a,b]- factors with prescribed properties. Furthermore, it is shown that the result in this paper is sharp.