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arXiv · 2607.16103

An improved upper bound for the planar Turán number of $C_8$

Xuqing Bai·Weichan Liu·Xiangxiang Nie·Xin Zhang
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Abstract

We prove that every $n$-vertex simple planar graph with no copy of $C_8$ has at most \[ \frac{69}{25}(n-2) \] edges, for every $n\ge 8$. This improves the best known bound \[ \frac{323}{108}n-6 \qquad \text{for every } n\ge 27. \]

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Xuqing Bai, Weichan Liu, Xiangxiang Nie, Xin Zhang. 2026-07-17. An improved upper bound for the planar Turán number of $C_8$. https://arxiv.org/abs/2607.16103

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