Paired-Domination in Claw-Free Graphs with Minimum Degree at Least Four

Abstract

A paired-dominating set of a graph $G$ is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number is the minimum cardinality of a paired-dominating set of $G$. In this paper, we investigate the paired-domination number in claw-free graphs with minimum degree at least four. We show that a connected claw-free graph $G$ with minimum degree at least four has paired-domination number at most $\frac{4}{7}$ its order.