On the theta number of powers of cycle graphs

Christine Bachoc (1) , Arnaud Pêcher (2, 3) , Alain Thiery (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We give a closed formula for Lovasz theta number of the powers of cycle graphs and of their complements, the circular complete graphs. As a consequence, we establish that the circular chromatic number of a circular perfect graph is computable in polynomial time. We also derive an asymptotic estimate for this theta number.

Mots clés: theta number; circular complete graph; circular perfect graph

Domaines: Combinatoire [math.CO]

Christine Bachoc, Arnaud Pêcher, Alain Thiery. On the theta number of powers of cycle graphs. 2011. ⟨hal-00572897⟩