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Beyond Perfection: Computational Results for Superclasses

In: Facets of Combinatorial Optimization

Author

Listed:
  • Arnaud Pêcher

    (Université de Bordeaux, Laboratoire Bordelais de Recherche Informatique (LaBRI)/INRIA Sud-Ouest)

  • Annegret K. Wagler

    (Université Blaise Pascal (Clermont-Ferrand II), Laboratoire d’Informatique, de Modélisation et d’Optimisation des Systèmes (LIMOS)/CNRS)

Abstract

We arrived at the Zuse Institute Berlin, Annegret as doctoral student in 1995 and Arnaud as postdoc in 2001, both being already fascinated from the graph theoretical properties of perfect graphs. Through encouraging discussions with Martin, we learned about the manifold links of perfect graphs to other mathematical disciplines and the resulting algorithmic properties based on the theta number (where Martin got famous for, together with Laci Lovász and Lex Schrijver). This made us wonder whether perfect graphs are indeed completely unique and exceptional, or whether some of the properties and concepts can be generalized to larger graph classes, with similar algorithmic consequences—the starting point of a fruitful collaboration. Here, we answer this question affirmatively and report on the recently achieved results for some superclasses of perfect graphs, all relying on the polynomial time computability of the theta number. Finally, we give some reasons that the theta number plays a unique role in this context.

Suggested Citation

  • Arnaud Pêcher & Annegret K. Wagler, 2013. "Beyond Perfection: Computational Results for Superclasses," Springer Books, in: Michael Jünger & Gerhard Reinelt (ed.), Facets of Combinatorial Optimization, edition 127, pages 133-161, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-38189-8_6
    DOI: 10.1007/978-3-642-38189-8_6
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