Spectral radius and k-factor-critical graphs

2023/06/29 by Sizhong Zhou, Zhou, Sizhong, Zhiren Sun +3 · 4 citations
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2306.16849

Abstract

For a nonnegative integer k, a graph G is said to be k-factor-critical if G-Q admits a perfect matching for any Q⊆ V(G) with |Q|=k. In this article, we prove spectral radius conditions for the existence of k-factor-critical graphs. Our result generalises one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.

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