Opuscula Math. 33, no. 1 (2013), 19-28

Opuscula Mathematica

On vertex b-critical trees

Mostafa Blidia
Noureddine Ikhlef Eschouf
Frédéric Maffray

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.

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  • Mostafa Blidia
  • University of Blida, LAMDA-RO, Department of Mathematics, B.P. 270, Blida, Algeria
  • Noureddine Ikhlef Eschouf
  • Dr. Yahia Fares University of Médéa, Faculty of Science and Technology, Department of G.E.I., Algeria
  • Frédéric Maffray
  • Grenoble-INP, Université Joseph Fourier, C.N.R.S, Laboratoire G-SCOP, Grenoble, France
  • Received: 2011-05-09.
  • Revised: 2012-03-08.
  • Accepted: 2012-09-18.
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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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