On the Number of Crossings in a Complete Graph
Frank Harary, Anthony Hill · Proceedings of the Edinburgh Mathematical Society · 1963
The purpose of this article is to describe two problems which involve drawing graphs in the plane. We will discuss both complete graphs and complete bicoloured graphs. The complete graphKn with n points or vertices has a line or edge joining every pair of distinct points, as shown in fig. 1 for n = 2, 3, 4, 5, 6.