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arXiv · 2208.13477

Extremal planar graphs with no cycles of particular lengths

Ervin Győri·Xianzhi Wang·Zeyu Zheng
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Abstract

In this paper we estimate the planar Turán number $\mathrm{ex}_\mathcal{P}(n,H)$ of some graphs $H$, i.e., the maximum number of edges in a planar graph $G$ of $n$ vertices not containing $H$ as a subgraph. We give a new, short proof when $H=C_5$, and study the cases when $G$ is bipartite or triangle-free and $H$ is a short even cycle. The proofs are mostly new applications or variants of the "contribution method" introduced by Ghosh, Győri, Martin, Paulos and Xiao in arXiv:2004.14094.

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Ervin Győri, Xianzhi Wang, Zeyu Zheng. 2022-08-30. Extremal planar graphs with no cycles of particular lengths. https://arxiv.org/abs/2208.13477

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