On the theta number of powers of cycle graphs

Christine Bachoc (1, 2) , Arnaud Pêcher (3) , Alain Thiéry (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 Lovász's theta number of the powers of cycle graphs $C_k^d$ and of their complements, the circular complete graphs $K_{k/d}$. 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 the theta number of $C_k^d$.

Domaines: Théorie des nombres [math.NT]; Combinatoire [math.CO]; Sciences de l'information et de la communication

Christine Bachoc, Arnaud Pêcher, Alain Thiéry. On the theta number of powers of cycle graphs. Combinatorica, 2013, 33 (3), pp.297-317. ⟨10.1007/s00493-013-2950-x⟩. ⟨hal-01003633⟩