Opuscula Mathematica
Opuscula Math. 33, no. 1 (), 19-28
http://dx.doi.org/10.7494/OpMath.2013.33.1.19
Opuscula Mathematica

On vertex b-critical trees




Abstract. A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph \(G\) is the largest \(k\) such that \(G\) admits a b-coloring with \(k\) colors. A graph \(G\) is b-critical if the removal of any vertex of \(G\) decreases the b-chromatic number. We prove various properties of b-critical trees. In particular, we characterize b-critical trees.
Keywords: b-coloring, b-critical graphs, b-critical trees.
Mathematics Subject Classification: 05C15.
Cite this article as:
Mostafa Blidia, Noureddine Ikhlef Eschouf, Frédéric Maffray, On vertex b-critical trees, Opuscula Math. 33, no. 1 (2013), 19-28, http://dx.doi.org/10.7494/OpMath.2013.33.1.19
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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