On Existence of $[a,b]$-Factors Avoiding Given Subgraphs

Abstract

For a graph $G=(V(G),E(G))$, let $i(G)$ be the number of isolated vertices in $G$. The isolated toughness of $G$ is defined as
$I(G)=min\{\frac{|S|}{i(G-S)}:S\subseteq V(G),i(G-S)\ge 2\}$ if $G$ is not complete; $I(G)=|V(G)|-1$ otherwise. In this paper, several sufficient conditions in terms of isolated toughness are obtained for the existence of $[a,b]$-factors avoiding given subgraphs, e.g., a set of vertices, a set of edges and a matching, respectively.