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Strengthening the Lovász bound for graph coloring

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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.

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

    Philippe Meurdesoif

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  1. Philippe Meurdesoif
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Correspondence to Philippe Meurdesoif.

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Meurdesoif, P. Strengthening the Lovász bound for graph coloring. Math. Program. 102, 577–588 (2005). https://doi.org/10.1007/s101070100246

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