J4 ›› 2008, Vol. 43 ›› Issue (5): 93-96 .doi:

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

PAN Rui-xia1， LAN Mei2， LIU Gui-zhen1   

  1. 1. School of Mathematics and System Science, Shandong University, Jinan 250100, Shandong, China;2. Department of Finance and Economics, Jinan Training College, Jinan 250103, Shandong, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: PAN Rui-xia

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Abstract:

The relationships between the isolated toughness I(G) and the existence of fractional ［a,b］-factors were given. It was proved thatif 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.

Key words: graph; isolated toughness; fractional ［a,b］-factors

CLC Number: 

  • O157.5
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