【摘要】 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)=∞。论文给出了图的分数[a,b]-因子的存在性与图的孤立韧度的关系。证明若δ(G)≥I(G)≥a-1+a/b,则图G有分数[a,b]-因子,其中a<b均为正整数。进一步地,证明了该结果在一定意义下是最好的。更多还原

【Abstract】 The isolated toughness of G is defined as I(G)=min{|S|/i(G-S):SV(G),i(G-S)≥2} if G is not complete.Otherwise,set I(G)=∞.In this paper,the relationships between the isolated toughness and the existence of fractional [a,b]-factors are given.It is proved that if δ(G)≥I(G)≥a-1+a/b,then G has a fractional [a,b]-factor where a<b.Furthermore,it is showed that the results in this paper are best possible in some sense.更多还原