设g是一个图,n,k和d是三个非负整数,满足n+2k+d≤|V(g)|-2,|V(g)|和n+d有相同的奇偶性.如果删去g中任意n个点后所得的图有k-匹配,并且任一k-匹配都可以扩充为一个亏d-匹配,那么称g是一个(n,k,d)-图.lIu和yu首先引入了(n,k,d)-图的概念,并且给出了(n,k,d)-图的一个刻划和若干性质.(0,k,1)-图也称为几乎k-可扩图.在本文中,作者改进了(n,k,d)-图的刻划,并给出了几乎k-可扩图和几乎k-可扩二部图的刻划,进而研究了几乎k-可扩图与n-因子临界图之间的关系.Let G be a graph,and let n,k and d be three nonnegative integers such that n+2k+ d≤|V(G) |-2 and,|V(G) | and n + d have the same parity.If after deleting any n vertices from G the remaining subgraph of G contains an k-matching and each k-matching of the subgraph can be extended to a defect-d-matching of the subgraph,then G is called an(n,k,d)-graph.Liu and Yu--([1]) first introduced(n,k,d)-graphs,and gave some properties and characterization of(n,k,d)-graphs.A(0,k,1)-graph may be also called a near k-extendable graph.In the present paper,the authors improve the characterization of(n,k,d)-graphs,and consequently obtain a characterization of near k-extendable graphs.Furthermore,a characterization of near k-extendable bipartite graphs and the relations between near k-extendable graphs and n-factor critical graphs are investigated.国家自然科学基金(10831001);福建省教育厅科技项目(JA08223)资
