Combinatorics/Game theory
A characterization of be-critical trees
Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 115-120.

The b-chromatic number of a graph G is the largest integer k such that G admits a proper coloring with k colors for which each color class contains a vertex that has at least one neighbor in all the other $k−1$ color classes. A graph G is called $be$-critical if the contraction of any edge e of G decreases the b-chromatic number of G. The purpose of this paper is the characterization of all $be$-critical trees.

Le nombre b-chromatique d'un graphe G est le plus grand entier k tel que G admette une coloration propre avec k couleurs, pour laquelle toute classe de couleur contient un sommet qui a au moins un voisin dans toutes les autres $k−1$ classes de couleur. Un graphe G est appelé $be$-critique si la contraction de toute arête e de G fait diminuer le nombre b-chromatique de G. Le but de cet article est la caractérisation de tous les arbres $be$-critiques.

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DOI: 10.1016/j.crma.2018.01.006
Bendali-Braham, Amel 1; Ikhlef-Eschouf, Noureddine 2; Blidia, Mostafa 3

1 Laboratory of Mechanics, Physics and Mathematical Modeling, Faculty of Sciences, University of Médéa, Algeria
2 Department of Mathematics and Computer Science, Faculty of Sciences, University of Médéa, Algeria
3 Laboratory LAMDA-RO, Department of Mathematics, University of Blida 1, B.P. 270, Blida, Algeria
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Bendali-Braham, Amel; Ikhlef-Eschouf, Noureddine; Blidia, Mostafa. A characterization of be-critical trees. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 115-120. doi : 10.1016/j.crma.2018.01.006. http://www.numdam.org/articles/10.1016/j.crma.2018.01.006/

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