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.

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.

REFERENCES

Fiorini, S. and Wilson, R. Edge-Colourings of Graphs. Pittman, 1977.

Nemhauser, G. L. and Park, S. "A Polyhedral Approach to Edge Coloring." Operations Res. Lett. 10, 315-322, 1991.

Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, p. 13, 1986.

Skiena, S. "Edge Colorings." §5.5.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 216, 1990.