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arXiv · 2602.21577

Spectral radius, toughness and $k$-factor of graphs

Yuanyuan Chen·Huiqiu Lin·Shucheng Li
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Abstract

A $k$-regular spanning subgraph of $G$ is called a $k$-factor. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] presented a tight sufficient condition in terms of the spectral radius for a connected 1-tough graph to contain a connected 2-factor (Hamilton cycle). Then it is interesting to consider the following problem: What is the spectral radius condition to guarantee the existence of a $k$-factor with $k\ge3$ in a connected 1-tough graph $G$ with $δ(G)\ge k$? In this paper, we completely solve this problem.

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Yuanyuan Chen, Huiqiu Lin, Shucheng Li. 2026-03-22. Spectral radius, toughness and $k$-factor of graphs. https://arxiv.org/abs/2602.21577

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