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

Yuanyuan Chen; Huiqiu Lin; Shucheng Li

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

Combinatorics 2026-03-24 v3

Authors: Yuanyuan Chen , Huiqiu Lin , Shucheng Li

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 $\delta(G)\ge k$ ? In this paper, we completely solve this problem.

Keywords

spectral radius toughness k-factor graph Hamilton cycle

Cite

@article{arxiv.2602.21577,
  title  = {Spectral radius, toughness and $k$-factor of graphs},
  author = {Yuanyuan Chen and Huiqiu Lin and Shucheng Li},
  journal= {arXiv preprint arXiv:2602.21577},
  year   = {2026}
}

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

Abstract

Keywords

Cite

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