### The b-continuity of graphs with large girth

**2016-02-03**

1602.01298 | math.CO

A b-coloring of the vertices of a graph is a proper coloring where each color
class contains a vertex which is adjacent to each other color class. The
b-chromatic number of $G$ is the maximum integer $b(G)$ for which $G$ has a
b-coloring with $b(G)$ colors. A graph $G$ is b-continuous if $G$ has a
b-coloring with $k$ colors, for every integer $k$ in the interval
$[\chi(G),b(G)]$. It is known that not all graphs are b-continuous. In this
article, we show that if $G$ has girth at least 10, then $G$ is b-continuous.

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