Section: New Results

On the Theta number of powers of cycle graphs

In [17] 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 $C_k^d$.