A Characterization of $P_6$-Free Irredundance Perfect Graphs

Vadim Zverovich; Pavel Skums; Lutz Volkmann

A Characterization of $P_6$-Free Irredundance Perfect Graphs

Combinatorics 2026-03-26 v1

Authors: Vadim Zverovich , Pavel Skums , Lutz Volkmann

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.

Keywords

irredundance perfect graphs $P_6$-free forbidden induced subgraphs domination number graph characterization

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@article{arxiv.2603.14668,
  title  = {A Characterization of $P_6$-Free Irredundance Perfect Graphs},
  author = {Vadim Zverovich and Pavel Skums and Lutz Volkmann},
  journal= {arXiv preprint arXiv:2603.14668},
  year   = {2026}
}

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21 pages

A Characterization of $P_6$-Free Irredundance Perfect Graphs

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