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

Dandan Fan; Huiqiu Lin; Yinfen Zhu

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arXiv · 2509.00769

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

Dandan Fan·Huiqiu Lin·Yinfen Zhu

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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 $\delta(G) \geq a$, where $b > a \geq 1$. This result resolves a problem posed by Hao and Li [Electron. J. Combin. (2024)].

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Dandan Fan, Huiqiu Lin, Yinfen Zhu. 2025-08-31. A note on the spectral radius and $[a,b]$-factor of graphs. https://arxiv.org/abs/2509.00769

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