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

Abstract

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 $\hat{I}´(G)\ge a$, where $b>a\ge 1$. This result resolves a problem posed by Hao and Li [Electron. J. Combin. (2024)].