分数k-因子临界图的条件

设G是-个连通简单无向图，如果删去G的任意k个项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．

Conditions of a graph being fractional k-factor-critical

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.