A main result in combinatorial optimization is that clique and chromatic number of a perfect
graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). The
circular-clique and circular-chromatic number are well-studied refinements of these graph
parameters, and circular-perfect graphs form the corresponding superclass of perfect
graphs. So far, it is unknown whether the (weighted) circular-clique and circular-chromatic
number of a circular-perfect graph are computable in polynomial time. In this paper, we …