边可消去图的[a,b]-因子的存在性

THE EXISTENCE OF [a,b]-FACTORS IN EDGE-DELETION GRAPHS

图G的孤立韧度定义为I(G)=min{|S|/i(G-S)|S■V(G),i(G-S)≥2},若G不是完全图;否则,令I(G)=|V(G)|-1.本文证明了:若G的最小度满足δ(G)≥a+n以及孤立韧度I(G)≥a-1+(a+2n)/b,其中a,b,n都是非负整数且1≤a<b.则对G的任意一个n条边的对集M,G-M有[a,b]-因子存在.同时对边可消去图中的星因子的存在性也进行了讨论.

The isolated toughness of G is defined as I（G） = min {｜S｜/i（ G - S）｜Slohtain in V（G）, i（ G - S） ≥2}; otherwise, I（G） = ｜ V（G） ｜ - 1. It is proved that if G is a graph with δ（G） ≥ a ＋ n and the isolated toughness/（G） ≥a-1＋a＋2n/b , where 1 ≤ a 〈 b. and n are non - negative integers. Then for any matching M with size n, G - M has [ a, b ] - factors. A sufficient condition for the star- factor in edge - deletion graph is also investigated.