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On the coloration of perfect graphs

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Recent Advances in Algorithms and Combinatorics

Abstract

We consider only finite graphs, without loops. Given an undirected graph G = (V, E), a k-coloring of the vertices of G is a mapping c: V → {1, 2,..., k} for which every edge xy of G has c(x) ≠ c(y). If c(v) = i we say that v has color i. Those sets c-1(T) (i = 1,..., k) that are not empty are called the color classes of the coloring c. Each color class is clearly a stable set (i.e., a subset of vertices with no edge between any two of them), hence we will frequently view a coloring as a partition into stable sets. The graph G is called k-colorable if it admits a k-coloring, and the chromatic number of G, denoted by χ(G), is the smallest integer k such that G is k-colorable. We refer to [9, 16, 29] for general results on graph theory.

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  1. F. Maffray
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Editors and Affiliations

  1. Equipe Combinatoire, CNRS, Paris, France

    Bruce A. Reed

  2. McGill University, Montreal, Canada

    Bruce A. Reed

  3. Departamento de Computacao—LIA, Universidade Federal do Ceara, Campus do Pici—Bloco 910, CEP 60455-760, Fortaleza, CE, Brasil

    Cláudia L. Sales

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Maffray, F. (2003). On the coloration of perfect graphs. In: Reed, B.A., Sales, C.L. (eds) Recent Advances in Algorithms and Combinatorics. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/0-387-22444-0_3

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