Determination of Chromatic Number The chromatic number χ of a graph is the smallest number of colors that can be assigned to the vertices of the graph such that no two adjacent vertices are assigned the same color. Thus far, no economic algorithm has been found that calculates χ for all graphs. Algorithms (that compute χ exactly) and heuristics (that have been developed to obtain a good estimate of χ in a more realistic timeframe) have been investigated and presented. Several of these heuristics, as well as a new variation, have been programmed on a microcomputer to color randomly generated unlabeled graphs for comparison purposes. These heuristics can be applied to find workable solutions to such problems as scheduling time tables and the storage/transportation of products.