Category:Definitions/Graph Colorings

This category contains definitions related to Graph Colorings.
Related results can be found in Category:Graph Colorings.

Vertex Coloring

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.

Edge Coloring

An edge $k$-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 edge in $E$.

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

A graph with such a coloring is called an edge-colored graph.