On the theta number of powers of cycle graphs
Christine Bachoc (IMB), Arnaud P\^echer (INRIA Bordeaux - Sud-Ouest,, LaBRI), Alain Thi\'ery (IMB)
TL;DR
This paper derives a closed-form formula for the Lovasz theta number of powers of cycle graphs and their complements, leading to polynomial-time computability of the circular chromatic number for circular perfect graphs.
Contribution
It provides a new closed-form expression for the theta number of certain graph classes and demonstrates polynomial-time computability of the circular chromatic number for circular perfect graphs.
Findings
Closed-form formula for Lovasz theta number of powers of cycle graphs.
Polynomial-time algorithm for computing the circular chromatic number of circular perfect graphs.
Asymptotic estimates for the theta number of these graph classes.
Abstract
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.
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