1. The problem statement, all variables and given/known data There are n amount of wi-fi networks in a given neighborhood. For every pair that are within 50 yards, the frequency used must be different, otherwise there will be interference. How few frequencies are required so that every wi-fi network can be assigned a frequency without interference? Express this problem as a graph theoretic optimization problem. 3. The attempt at a solution So I believe I can turn this into a k-colorable problem in which the networks are the vertices and the edges are the pairs within 50 yards. Then find the smallest k for which this graph would be k-colorable. I'm wondering if there is a way express this in a more mathematical manner, with an objective function and with constraints. Maybe an integer program? I'm not quite sure. Any help is much appreciated.