The Solution of the Graph-Coloring Problem as a Set-Covering Problem

The minimum number of channels required to satisfy the frequency assignment constraints of a collection of equipments for which specified pairs of equipments are denied cochannel operation has been shown to be equal to the chromatic number of an associated graph. This paper provides a formulation of the graph-coloring problem in terms of a related problem for which efficient computer programs have been prepared. This related problem is known as the zero-one set covering problem in which the rows of a binary array are "covered" with the minimum number of columns such that every row contains at least one nonzero element in a column belonging to the cover.