Upper bounds on the b-chromatic number and results for restricted graph classes
Mais Alkhateeb ; Anja Kohl
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 709-735 / Harvested from The Polish Digital Mathematics Library
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A b-coloring of a graph G by k colors is a proper vertex coloring such that every color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number χb(G) is the maximum integer k for which G has a b-coloring by k colors. Moreover, the graph G is called b-continuous if G admits a b-coloring by k colors for all k satisfying χ(G)≤k≤χb(G). In this paper, we establish four general upper bounds on χb(G). We present results on the b-chromatic number and the b-continuity problem for special graphs, in particular for disconnected graphs and graphs with independence number 2. Moreover we determine χb(G) for graphs G with minimum degree δ(G) ≥ |V(G)|-3, graphs G with clique number ω(G) ≥ |V(G)|-3, and graphs G with independence number α(G) ≥ |V(G)|-2. We also prove that these graphs are b-continuous.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:271042 
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Mais Alkhateeb; Anja Kohl. Upper bounds on the b-chromatic number and results for restricted graph classes. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 709-735. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1575/

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