vix.ing · top · new · best · stats · spec

Strongly Perfect Claw-free Graphs -- A Short Proof

2019/12/11 by Chudnovsky, Maria, Dibek, Cemil
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.05645

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.

Related