The strong perfect graph conjecture for pan-free graphs
A graph \(G\) is perfect if for every induced subgraph \(F\) of \(G\), the chromatic number \(\chi(F)\) equals the largest number \(\omega(F)\) of pairwise adjacent vertices in \(F\). Berge's famous Strong perfect graph conjecture asserts that a graph \(G\) is perfect if and only if neither \(G\) nor its complement \(\overline{G}\) contains an odd chordless cycle of length at least five. Its resolution has eluded researchers for more than twenty years. We prove that the conjecture is true for a class of graphs which strictly contains the claw-free graphs.
scientific article; zbMATH DE number 4079480