Abstract for talk by Márcia Cerioli

Title: On the b-continuity of graphs

A b-coloring of a graph is a (proper) coloring of its vertices such that for each color class there is at least one vertex that is adjacent to all possible colors. A k-b-coloring is a b-coloring on k colors.

One peculiar characteristic of b-colorings is that for some graphs there is an integer k such that G has both a k-1 and a (k+1)-b-coloring but does not have any k-b-colorings. Otherwise, G is called a b-continuous graph.

In this talk I will survey results concerning b-continuity of graphs belonging to special graph classes.