Definition:Coloring/Edge Coloring

Definition
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.

Also see

 * Definition:Undirected Network: An edge-colored graph can be considered as an undirected network in which the colors correspond to numbers.

However, in an edge-colored graph, the actual values of the numbers is unimportant.


 * proper coloring, in which adjacent edges are required to have different colors.