On vertex b-critical trees
Mostafa Blidia, Noureddine Ikhlef Eschouf, Frédéric Maffray · Opuscula Mathematica · 2012
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.