【摘要】 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。更多还原

【Abstract】 The relationships between the isolated toughness I(G) and the existence 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.更多还原