Some sufficient conditions for a graph with minimum degree to be $k$-critical with respect to $[1,b]$-odd factors

Abstract

A graph $G$ is $k$-factor-critical if $G-S$ has a perfect matching for every subset $S\subseteq V(G)$ with $|S|=k$. A spanning subgraph $H$ of $G$ is called a $[1,b]$-odd factor if $b\equiv 1(\mathrm{mod}2)$ and $d_H(v)\in \left\{1,3,\dots ,b\right\}$ for every $v\in V(G),$ where $d_H(v)$ denotes the degree of vertex $v$ in $H$. Moreover, $G$ is said to be $k$-critical with respect to $[1,b]$-odd factors if $G-X$ contains a $[1,b]$-odd factor for every subset $X\subseteq V(G)$ with $|X|=k$. In this paper, we provide some sufficient conditions based on the distance spectral radius and the distance signless Laplacian spectral radius for a graph with minimum degree to be $k$-critical with respect to $[1,b]$-odd factors.