Spectral conditions for graphs to contain k-factors

2025/08/05 by Tang, Xinying, Zhang, Wenqian · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05678

Abstract

Let G be a graph. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For an integer k≥1, a k-factor of G is a k-regular spanning subgraph of G. Assume that k and n are integers satisfying k≥2,kn≡0~(\mod2) and n≥max\k²+6k+7,20k+10\. Let G be a graph of order n and with minimum degree at least k. In this paper, we give a sharp lower bound of ρ(G) to guarantee that G contains a k-factor.

Citations

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

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