Definition:Coloring/Vertex Coloring

Definition
A vertex $k$-coloring of a simple graph $G = \left({V, E}\right)$ is defined as an assignment of one element from a set $C$ of $k$ colors to each vertex in $V$.

That is, a vertex $k$-coloring of the graph $G = \left({V, E}\right)$ is a mapping $c: V \to \left\{{1, 2, \ldots k}\right\}$.

A graph with such a coloring is called a vertex-colored graph.

Also see

 * Definition:Labeled Graph: a vertex-colored graph can be considered as a labeled graph in which the labels are considered as colors.


 * Definition:Proper Coloring, in which adjacent vertices or edges are required to have different colors.