Resumen de The strong perfect graph theorem
Neil Robertson, Robin Thomas, Maria Chudnovsky, Paul D. Seymour
A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. The ¿strong perfect graph conjecture¿ (Berge, 1961) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by Conforti, Cornu¿ejols and Vu¡skovi¿c ¿ that every Berge graph either falls into one of a few basic classes, or admits one of a few kinds of separation (designed so that a minimum counterexample to Berge¿s conjecture cannot have either of these properties). In this paper we prove both of these conjectures.
