Polynomial time computability of some graph parameters for superclasses of perfect graphs
by Arnaud Pêcher; Annegret K. Wagler
International Journal of Mathematics in Operational Research (IJMOR), Vol. 4, No. 3, 2012

Abstract: A main result in combinatorial optimisation is that clique and chromatic number of a perfect graph are computable in polynomial time (Grötschel 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.

Online publication date: Wed, 02-May-2012

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