Unavoidable cycle lengths in graphs

被引：7
|
作者：
Verstraete, J [1 ]
机构：
[1] Univ Waterloo, Dept Combinat & Optimaz, Waterloo, ON N2L 3G1, Canada
来源：
JOURNAL OF GRAPH THEORY | 2005年 / 49卷 / 02期
关键词：
unavoidable cycle lengths; longest cycle; k-connected; binomial distribution;
D O I：
10.1002/jgt.20072
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An old conjecture of Erdos states that there exists an absolute constant c and a set S of density zero such that every graph of average degree at least c contains a cycle of length in S. In this paper, we prove this conjecture by showing that every graph of average degree at least ten contains a cycle of length in a prescribed set S satisfying | S ∧ {1, 2,..., n}| = O(n(0.99)). © 2005 Wiley Periodicals, Inc.
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页码：151 / 167
页数：17
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