Abstract
A main result in combinatorial optimisation is that clique and chromatic number of a perfect graph are computable in polynomial time (Grotschel et al., 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 clique, circular-clique, circular-chromatic and chromatic numbers of a circular-perfect graph are computable in polynomial time. In this paper, we show the polynomial time computability of these graph parameters for some classes of circular-perfect graphs with the help of polyhedral arguments.
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