Minimum Edge Coloring

An edge coloring of a graph is a coloring of the edges of such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring containing the smallest possible number of colors for a given graph is known as a minimum edge coloring.

Finding the minimum edge coloring of a graph is equivalent to finding the minimum vertex coloring of its line graph (Skiena 1990, p. 216).

Computation of a minimum edge coloring of a graph is implemented in the Wolfram Language as FindEdgeColoring[g].

The edge chromatic number gives the minimum number of colors with which a graph can be colored, i.e., the number of colors in a minimum edge coloring.