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arXiv · 2606.13131

The planar Turán number of $\{K_{4},Θ_{6}^{i}\}$

Jing Chen·Kai Gao·Yongxin Lan·Changqing Xu·Shaoyu Zhao
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Abstract

Let $\mathcal{H}$ be a family of graphs. A graph is said to be $\mathcal{H}$-free if it contains no subgraph isomorphic to a graph in $\mathcal{H}$. The planar Turán number $ex_{_\mathcal{P}}(n,\mathcal{H})$ is defined as the maximum number of edges in an $\mathcal{H}$-free planar graph on $n$ vertices. In this paper, we determine the exact value of $ex_{_\mathcal{P}}(n,\{K_{4}, Θ_{6}^{1}\})$ and a tight upper bound of $ex_{_\mathcal{P}}(n,\{K_{4}, Θ_{6}^{2}\})$.

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Jing Chen, Kai Gao, Yongxin Lan, Changqing Xu, Shaoyu Zhao. 2026-06-11. The planar Turán number of $\{K_{4},Θ_{6}^{i}\}$. https://arxiv.org/abs/2606.13131

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