# Upper bounds on the b-chromatic number and results for restricted graph classes

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 4, page 709-735
- ISSN: 2083-5892

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topMais Alkhateeb, and Anja Kohl. "Upper bounds on the b-chromatic number and results for restricted graph classes." Discussiones Mathematicae Graph Theory 31.4 (2011): 709-735. <http://eudml.org/doc/271042>.

@article{MaisAlkhateeb2011,

abstract = {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 $χ_b(G)$ 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 $χ(G) ≤ k ≤ χ_b(G)$. In this paper, we establish four general upper bounds on $χ_b(G)$. 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 $χ_b(G)$ 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.},

author = {Mais Alkhateeb, Anja Kohl},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {coloring; b-coloring; b-chromatic number; b-continuity; -coloring; -chromatic number; -continuity},

language = {eng},

number = {4},

pages = {709-735},

title = {Upper bounds on the b-chromatic number and results for restricted graph classes},

url = {http://eudml.org/doc/271042},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Mais Alkhateeb

AU - Anja Kohl

TI - Upper bounds on the b-chromatic number and results for restricted graph classes

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 4

SP - 709

EP - 735

AB - 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 $χ_b(G)$ 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 $χ(G) ≤ k ≤ χ_b(G)$. In this paper, we establish four general upper bounds on $χ_b(G)$. 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 $χ_b(G)$ 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.

LA - eng

KW - coloring; b-coloring; b-chromatic number; b-continuity; -coloring; -chromatic number; -continuity

UR - http://eudml.org/doc/271042

ER -

## References

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