# A planar graph is a graph that can be drawn on a sheet of paper so that no two edges cross. Show that the complete graph K 4 with four vertices is planar. The complete graph K 5 with five vertices is not planar. Make this plausible by attempting to draw K 5 so that no edges cross. Interpret the

Chapter 23, PROBLEM SET 23.8 #17

A planar graph is a graph that can be drawn on a sheet of paper so that no two edges cross. Show that the complete graph K_{4} with four vertices is planar. The complete graph K_{5} with five vertices is not planar. Make this plausible by attempting to draw K_{5} so that no edges cross. Interpret the result in terms of a net of roads between five cities.

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