分数k-因子临界图的条件(英文)

Conditions of a graph being fractional k-factor-critical

设G是一个连通简单无向图,如果删去G的任意k个顶点后的图有分数完美匹配,则称G是分数k-因子临界图.给出了G是分数k-因子临界图的韧度充分条件与度和充分条件,这些条件中的界是可达的,并给出G是分数k-因子临界图的一个关于分数匹配数的充分必要条件.

Let G be a connected undirected simple graph. If the remaining subgraph still has a fractional perfect matching after deleting any k vertices of G, the graph G is said to be fractional k-factor-critical. This paper gives sufficient conditions in terms of the toughness and the degree sum for a graph G to be fractional k-factor-critical. In some sense, we prove that the conditions are best possible. Besides, we give a necessary and sufficient condition in terms of the fractional matching number for a graph G to be fractional k-factor-critical.