On the theta number of powers of cycle graphs

Authors:
Christine Bachoc;Arnaud Pêcher;Alain Thiéry
Affiliations:
Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux I, Talence, France 33405;Laboratoire Bordelais de Recherche Informatique (LaBRI) / INRIA Sud-Ouest, Université Bordeaux I, Talence, France 33405;Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux I, Talence, France 33405
Venue:
Combinatorica
Year:
2013

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Abstract

We give a closed formula for Lovász's theta number of the powers of cycle graphs C k d驴1 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 .