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Polynomial time computability of some graph parameters for superclasses of perfect graphs

Author

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  • Arnaud Pêcher
  • Annegret K. Wagler

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.

Suggested Citation

  • Arnaud Pêcher & Annegret K. Wagler, 2012. "Polynomial time computability of some graph parameters for superclasses of perfect graphs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(3), pages 263-275.
    • Handle: RePEc:ids:ijmore:v:4:y:2012:i:3:p:263-275
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