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

2025/08/31 by Dandan Fan, Huiqiu Lin, Fan, Dandan +3 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2509.00769

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Spectral conditions for graphs to contain k-factors
• Spectral radius, fractional [a,b]-factor and ID-factor-critical graphs
• Spectral conditions for k-extendability and k-factors of bipartite graphs
• Spectral radius and [a,b]-factors in graphs
• Sharp conditions for the existence of an even [a,b]-factor in a graph

Cited by

• Spectral extremal problems for (a,b,k)-critical and fractional (a,b,k)-critical graphs

Related

• Spectral radius and [a,b]-factors in graphs
• The existence of even factors based on the A_α-spectral radius of graphs
• Spectral conditions for graphs to contain k-factors
• Spectral Sufficient Conditions for Graph Factors
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