Strongly Perfect Claw-free Graphs -- A Short Proof

TL;DR

This paper provides a shorter proof for the characterization of claw-free graphs that are strongly perfect, confirming a conjecture from 1990 and simplifying previous proofs.

Contribution

It offers a more concise proof of the known characterization of strongly perfect claw-free graphs, improving upon Wang's 2006 result.

Findings

Confirmed the characterization of strongly perfect claw-free graphs

Provided a shorter, more elegant proof of the existing theorem

Simplified the understanding of the structure of these graphs

Abstract

A graph is strongly perfect if every induced subgraph H has a stable set that meets every maximal clique of H. A graph is claw-free if no vertex has three pairwise non-adjacent neighbors. The characterization of claw-free graphs that are strongly perfect by a set of forbidden induced subgraphs was conjectured by Ravindra in 1990 and was proved by Wang in 2006. Here we give a shorter proof of this characterization.