  A b-coloring of a graph is a proper coloring of its vertices such that each
color class contains a vertex adjacent to at least one vertex of every other
color class. The b-chromatic number of a graph is the largest integer k such
that the graph has a b-coloring with k colors. In this work we present lower
bounds for the b-chromatic number of a vertex-deleted subgraph of a graph,
particularly regarding two important classes, quasi-line and chordal graphs. We
also get bounds for the b-chromatic number of G -{x}, when G is a graph with
large girth.
