Represent the problem as a graph with vertices as the stations and edges when two stations are close enough to cause interference. We are looking for the chromatic number of the graph. Vertices that are colored identically represent stations that can have the same frequency.

This graph has chromatic number 5. A proper 5-coloring is shown on the right. Notice that the graph contains a copy of the complete graph \(K_5\) so no fewer than 5 colors can be used.

A drawing of the graph representing the radio stations with edges between vertices if those radio stations interfere with each other. Vertices are arranged in a ring with KQEA at the top, and proceeding clockwise to KQEB, and so on through KQEH.
A drawing of the graph representing the radio stations with edges between vertices if those radio stations interfere with each other. Here each vertex is labeled with a letter representing a color. From the top vertex and moving around clockwise: R, G, B, B, G, G, Y, R, B, P. A copy of of the graph K5 is drawn in bold among the edges of the original graph.