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
\(I(G) = \min\left\{\frac{|S|}{i(G-S)}: S \subseteq V(G), i(G-S) \geq 2\right\}\) 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.