The strong perfect graph theorem

• Autores: Neil Robertson, Robin Thomas, Maria Chudnovsky, Paul D. Seymour
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 164, Nº 1, 2006, págs. 51-229
• Idioma: inglés
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• Resumen

  • 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.