A Characterization of $P_6$-Free Irredundance Perfect Graphs

TL;DR

This paper characterizes $P_6$-free irredundance perfect graphs by identifying eleven forbidden induced subgraphs, enhancing understanding of their structural properties.

Contribution

It provides a complete characterization of $P_6$-free irredundance perfect graphs through a set of eleven forbidden induced subgraphs.

Findings

Characterization of $P_6$-free irredundance perfect graphs

Identification of eleven forbidden induced subgraphs

Structural insights into this graph class

Abstract

Let $ir(G)$ and $\gamma(G)$ be the irredundance number and the domination number of a graph $G$, respectively. A graph $G$ is called irredundance perfect if $ir(H)=\gamma(H)$ for every induced subgraph $H$ of $G$. The subclass of $P_6$-free irredundance perfect graphs has been studied extensively. In this paper, we present a characterization of this graph class in terms of eleven forbidden induced subgraphs.