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Graph Coloring

To describe graph-coloring in rigorous mathematical terms, let the set denote the nodes of an undirected graph and let denote the edges in , or . Graph edges are tuples , where and . The two nodes are defined to be neighbors if the tuple . Given a graph , we define a coloring of to be an assignment of colors to the nodes of such that no two adjacent nodes are given the same color. This can be restated as a coloring of is a mapping such that . The color of node i is and . The minimum possible value for is known as the chromatic number of , which we denote as [32].





David P. Koester
Sun Oct 22 17:27:14 EDT 1995