On b-vertex and b-edge critical graphs
Noureddine Ikhlef Eschouf, Mostafa Blidia · Opuscula Mathematica · 2014
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.