图的孤立韧度与分数k-消去图

Isolated Toughness and Fractional k-Deleted Graphs

设G是一个图,k(?) 2是一个整数,若对于图G的任一条边e,G-e都存在一个分数k-因子,则称G是一个分数k-消去图.图G的孤立韧度I(G)定义为:若G是完备图,I(G)=+∞;否则,I(G)=,其中i(G—S)表示G—s中的孤立点数目.本文证明了当I(G)>k,并且δ(G)(?)k+1时,G是分数k-消去图.

A graph G is fractional k-deleted if there exists a fractional k-factor after deleting any edge of G. The isolated toughness 7(G) is defined as follows: If G is a complete graph, then 7(G) = +∞; else, I(G) = min, where i(G - S) denotes the number of isolated vertices in G - S. In this paper, it is proved that G is fractional k-deleted if δ(G) (?) k + 1 and I(G) > k. We also proved that our result is best possible.