A vertex-colored graph is a graph together with an assignment of colors or labels to its vertices. This assignment
need not be a proper coloring, so adjacent
vertices need not have distinct colors unless this is stated explicitly. Thus
a vertex-colored graph need not define a vertex coloring
in the chromatic-number sense.
Vertex-colored graphs arise in problems asking for subgraphs with prescribed color patterns, such as colorful cycles
in which no color appears more than once.
