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arXiv · 2311.13323

Spectral condition for the existence of a chorded cycle

Jiaxin Zheng·Xueyi Huang·Junjie Wang
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Abstract

A chord of a cycle $C$ is an edge joining two non-consecutive vertices of $C$. A cycle $C$ in a graph $G$ is chorded if the vertex set of $C$ induces at least one chord. In this paper, we prove that if $G$ is a graph with order $n\geq 6$ and $ρ(G)\geq ρ(K_{2,n-2})$, then $G$ contains a chorded cycle unless $G\cong K_{2,n-2}$. This gives one answer to a question posed by Gould [Results and problems on chorded cycles: A survey, Graphs Combin. 38 (2022) 189].

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Jiaxin Zheng, Xueyi Huang, Junjie Wang. 2023-12-05. Spectral condition for the existence of a chorded cycle. https://arxiv.org/abs/2311.13323

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