A vertex-colored graph is a graph together with an assignment of colors or labels to its vertices. Unlike a vertex
coloring in the chromatic-number sense, a vertex-colored graph 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.
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.
