Tight bound on the minimum degree to guarantee graphs forbidding some odd cycles to be bipartite

IF 1 3区 数学 Q1 MATHEMATICS
Xiaoli Yuan, Yuejian Peng
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引用次数: 0

Abstract

Erdős and Simonovits asked the following question: For an integer r2 and a family of non-bipartite graphs H, determine the infimum of α such that any H-free n-vertex graph with minimum degree at least αn has chromatic number at most r. We answer this question for r=2 and any family consisting of odd cycles. Let C be a family of odd cycles in which C2+1 is the shortest odd cycle not in C and C2k+1 is the longest odd cycle in C, we show that if G is an n-vertex C-free graph with n1000k8 and δ(G)>max{n/(2(2+1)),2n/(2k+3)}, then G is bipartite. Moreover, this bound on the minimum degree is tight.
保证禁止某些奇数循环的图为两部分图的最小度数的严格约束
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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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