[a,b]-因子不包含给定独立集的充分条件

A sufficient condition for a graph to have[a,b]-factors excluding given independent set

设G是一个图且a、b为非负整数,a≤b。图G的一个[a,b]-因子是图G的一个支撑子图H,且满足对所有的x∈V(G),a≤dH(x)≤b都成立。文章研究了最小度与[a,b]因子之间的关系,证明了若δ(G)≥(a+b)n/(a+2b),那么G中总有[a,b]-因子不包含给定独立集I。

Let G be a graph and let a and b be nonnegative integers with a≤b. An [-a,b]-factor of G is defined as a spanning subgraph H of G such that a≤dH（x）≤b for each x∈V（G）. In this paper, it is proved that if δ（G）≥（n＋b）n/（a＋2b）, then G has an [a,b]-faetor excluding given independent set I.