# 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**.

## Pages in category "Definitions/Graph Colorings"

The following 6 pages are in this category, out of 6 total.