图存在分数[a，b]-因子的一个孤立韧度条件

A condition of isolated toughness on the existence of fractional [a,b]-factors of graphs

给出了图的孤立韧度I(G)与分数[a,b]-因子存在性间的关系,证明了若δ(G)≥I(G)≥a-1+(a-1)/b,其中a、b均为整数,2≤a<b,则图G有分数[a,b]-因子。进一步证明该结论在一定意义下是最好的,并且提出猜想当a=b时结论仍然成立。

Abstract： The relatiomhips between the isolated toughness I（G） and the exlstenee of fractional [a, b]-factors were given. It was proved that if δ （G） ≥ I（G） ≥ a - 1 ＋ （ a - 1 ） / b, then G has a fractional [ a, b ]-factor where 2 ≤ a 〈 b. The results are best possible in some sense. In addition a conjecture about a = b was given.