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arXiv · 2004.01162

The maximum number of induced $C_5$'s in a planar graph

Debarun Ghosh·Ervin Győri·Oliver Janzer·Addisu Paulos·Nika Salia·Oscar Zamora
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Abstract

Finding the maximum number of induced cycles of length $k$ in a graph on $n$ vertices has been one of the most intriguing open problems of Extremal Graph Theory. Recently Balogh, Hu, Lidický and Pfender answered the question in the case $k=5$. In this paper we determine precisely, for all sufficiently large $n$, the maximum number of induced $5$-cycles that an $n$-vertex planar graph can contain.

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Debarun Ghosh, Ervin Győri, Oliver Janzer, Addisu Paulos, Nika Salia, Oscar Zamora. 2021-09-08. The maximum number of induced $C_5$'s in a planar graph. https://arxiv.org/abs/2004.01162

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