Spectral radius and k-factor-critical graphs

TL;DR

This paper establishes spectral radius conditions that guarantee the existence of k-factor-critical graphs, generalizing previous results on perfect matchings and demonstrating the sharpness of these bounds.

Contribution

It introduces new spectral radius criteria for k-factor-critical graphs, extending known results on perfect matchings in graphs.

Findings

Spectral radius conditions ensure k-factor-criticality.

Bounds on spectral radius are proven to be sharp.

Generalizes previous perfect matching results.

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 $Q\subseteq V(G)$ 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.