The maximum number of odd cycles in a planar graph

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-11-10 DOI:10.1002/jgt.23197

Emily Heath, Ryan R. Martin, Chris Wells

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引用次数: 0

Abstract

How many copies of a fixed odd cycle, $C_{2 m + 1}$ , can a planar graph contain? We answer this question asymptotically for $m \in {2, 3, 4}$ and prove a bound which is tight up to a factor of 3/2 for all other values of $m$ . This extends the prior results of Cox and Martin and of Lv, Győri, He, Salia, Tompkins, and Zhu on the analogous question for even cycles. Our bounds result from a reduction to the following maximum likelihood question: which probability mass $μ$ on the edges of some clique maximizes the probability that $m$ edges sampled independently from $μ$ form either a cycle or a path?

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .