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arXiv · 2605.17330

The Outerplanar Tur\'{a}n Number of Double Stars

Chaofan Zhang·Yongxin Lan·Changqing Xu
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Abstract

Let $H$ be a nonempty graph. A graph is $H$-free if it does not contain any copy of $H$ as a subgraph. The outerplanar Tur\'{a}n number of $H$, denoted by $ex_{_\mathcal{OP}}(n,H)$, is the maximum number of edges among all $H$-free outerplanar graphs on $n$ vertices. A double star $S_{p,q}$ is the graph obtained from an edge by joining its two endpoints with $p$ and $q$ isolated vertices respectively, where $q \ge p\ge 1$. In this paper, we determine the exact values of $ex_{_\mathcal{OP}}(n,S_{p,q})$ for all $q\ge p\ge 2$, with the sole exception of $p=2$ and $q=3$; for the latter, we establish a lower bound.

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Chaofan Zhang, Yongxin Lan, Changqing Xu. 2026-05-17. The Outerplanar Tur\'{a}n Number of Double Stars. https://arxiv.org/abs/2605.17330

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