Strengthening the Lovász ** bound for graph coloring

  • Authors:

  • Philippe Meurdesoif

  • Affiliations:

  • Université Bordeaux 1, Mathématiques Appliquées de Bordeaux, 351 Cours de la Libération, 33405, Talence, France

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2005

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Abstract

The Lovász θ-number is a way to approximate the independence number of a graph, but also its chromatic number. We express the Lovász bound as the continuous relaxation of a discrete Lovász θ-number which we derive from Karger et al.’s formulation, and which is equal to the chromatic number. We also give another relaxation à la Schrijver-McEliece, which is better than the Lovász θ-number.