The investigation of eigenvalue conditions for the existence of an [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]-factors have attracted considerable attention. In this paper, we establish a spectral radius condition that ensures the existence of an [a,b]-factor in a graph G with minimum degree δ(G)≥a, where b>a≥1. This result resolves a problem posed by Hao and Li [Electron. J. Combin. (2024)].
@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}
}