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The ratio of the numbers of odd and even cycles in outerplanar graphs

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arxiv 2105.02361 v1 pith:K3IACMS3 submitted 2021-05-05 math.CO cs.DM

Akihiro Higashitani , Naoki Matsumoto This is my paper · ORCID
classification math.COcs.DM
keywords graphsratioouterplanarcyclesdivergeseveninfinitynumbers
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In this paper, we investigate the ratio of the numbers of odd and even cycles in outerplanar graphs. We verify that the ratio generally diverges to infinity as the order of a graph diverges to infinity. We also give sharp estimations of the ratio for several classes of outerplanar graphs, and obtain a constant upper bound of the ratio for some of them. Furthermore, we consider similar problems in graphs with some pairs of forbidden subgraphs/minors, and propose a challenging problem concerning claw-free graphs.

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