Problem

Source: IMO Shortlist 1989, Problem 17, ILL 59

Tags: combinatorics, graph theory, Extremal Graph Theory, IMO Shortlist



Given seven points in the plane, some of them are connected by segments such that: (i) among any three of the given points, two are connected by a segment; (ii) the number of segments is minimal. How many segments does a figure satisfying (i) and (ii) have? Give an example of such a figure.