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Article Dans Une Revue Discrete Applied Mathematics Année : 2007

On the B-Continuity Property of Graphs

Résumé

This paper deals with b-colorings of a graph G, that is, proper colorings in which for each color c, there exists at least one vertex colored by c such that its neighbors are colored by each other color. The b-chromatic number b(G) of a graph G is the maximum number of colors for which G has a b-coloring. It is easy to see that every graph G has a b-coloring using ?(G) colors. We say that G is b-continuous iff for each k, ?(G)less-than-or-equals, slantkless-than-or-equals, slantb(G), there exists a b-coloring with k colors. It is well known that not all graphs are b-continuous. We call b-spectrum Sb(G) of G to be the set of integers k for which there is a b-coloring of G by k colors. We show that for any finite integer set I, there exists a graph whose b-spectrum is I and we investigate the complexity of the problem of deciding whether a graph G is b-continuous, even if b-colorings using ?(G) and b(G) colors are given.

Dates et versions

hal-00126001 , version 1 (23-01-2007)

Identifiants

Citer

Dominique Barth, Johanne Cohen, Taoufik Faik. On the B-Continuity Property of Graphs. Discrete Applied Mathematics, 2007, 155 (13), pp.1761 - 1768. ⟨10.1016/j.dam.2007.04.011⟩. ⟨hal-00126001⟩
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