@Article{Eschouf2015,
author = "Eschouf, Noureddine Ikhlef and Blidia, Mostafa",
title = "On b-vertex and b-edge critical graphs",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "2",
pages = "171--180",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.2.171",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.2.171",
abstract = "A \(b\)-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the \(b\)-chromatic number \(b(G)\) of a graph \(G\) is the largest integer \(k\) such that \(G\) admits a \(b\)-coloring with \(k\) colors. A simple graph \(G\) is called \(b^{+}\)-vertex (edge) critical if the removal of any vertex (edge) of \(G\) increases its \(b\)-chromatic number. In this note, we explain some properties in \(b^{+}\)-vertex (edge) critical graphs, and we conclude with two open problems.",
keywords = "\(b\)-coloring, \(b\)-chromatic number, critical graphs",
issn = "1232-9274"
}