English

A note on the spectral radius and $[a,b]$-factor of graphs

Spectral Theory 2025-09-04 v2

Abstract

The investigation of eigenvalue conditions for the existence of an [a,b][a,b]-factor originates in the work of Brouwer and Haemers (2005) on perfect matchings. In the decades since, spectral extremal problems related to [a,b][a,b]-factors have attracted considerable attention. In this paper, we establish a spectral radius condition that ensures the existence of an [a,b][a,b]-factor in a graph GG with minimum degree δ(G)a\delta(G) \geq a, where b>a1b > a \geq 1. This result resolves a problem posed by Hao and Li [Electron. J. Combin. (2024)].

Keywords

Cite

@article{arxiv.2509.00769,
  title  = {A note on the spectral radius and $[a,b]$-factor of graphs},
  author = {Dandan Fan and Huiqiu Lin and Yinfen Zhu},
  journal= {arXiv preprint arXiv:2509.00769},
  year   = {2025}
}