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.
A (not necessarily minimum) edge coloring of a graph can be computed using EdgeColoring[g] in the Wolfram Language package Combinatorica` .
The edge chromatic number gives the minimum number of colors with which graph's edges can be colored.
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. 