Sufficient conditions for a graph with minimum degree to be k-critical with respect to [1,b]-odd factor

Abstract

A spanning subgraph $F$ of a graph $G$ is called a $[1,b]$-odd factor if $b\equiv 1$ (mod 2) and $d_F(v)\in \{1,3,\dots ,b\}$ for every $v\in V(G)$. A graph $G$ of order $n\ge k+2$ is $k$-critical with respect to $[1,b]$-odd factor if for any $X\subseteq V(G)$ with $|X|=k$, $G-X$ has a $[1,b]$-odd factor. In this paper, we provide a size and spectral radius conditions for a graph with minimum degree to be $k$-critical with respect to $[1,b]$-odd factor, respectively.

arXiv comment16 pages