Talking about colored graphs there is a definition given for graphs with bounded color valence. This definition is as follows:
A vertex-colored graph $G=(V,E)$ has bounded color valence, if there is a constant $D$, such that for every color class $C$ every vertex $v$ (possibly in $C$) has at most $D$ neighbors or at most $D$ non-neighbors in $C$.
It's hard for me understanding this definition. I can't think of an example for a graph that doesn't have bounded color valence, as e.g. one can assign a different color for every vertex.
Link to the definition: http://arxiv.org/pdf/1208.0142v2.pdf (p. 16)