Coloring perfect graphs with no balanced skew-partitions

Maria Chudnovsky (1) , Nicolas Trotignon (2, 3) , Théophile Trunck (3, 4) , Kristina Vušković (5)

1 Department of Computer Science [New York]
2 MC2 - Modèles de calcul, Complexité, Combinatoire
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
5 School of Computing [Leeds]

We present an $O(n^5)$ algorithm that computes a maximum stable set of any perfect graph with no balanced skew-partition. We present $O(n^7)$ time algorithm that colors them.

Mots clés: Perfect graphs; Berge graphs; Coloring; Maximum stable set; 2-join; Skew partition; Homogeneous pair

Domaines: Informatique [cs]

Maria Chudnovsky, Nicolas Trotignon, Théophile Trunck, Kristina Vušković. Coloring perfect graphs with no balanced skew-partitions. Journal of Combinatorial Theory, Series B, 2015, 115, pp.26-65. ⟨10.1016/j.jctb.2015.04.007⟩. ⟨hal-01222922⟩