MathDB
Maximal number of segments - [ILL 1977]

Source:

January 11, 2011
combinatorics proposedcombinatorics

Problem Statement

We are given nn points in space. Some pairs of these points are connected by line segments so that the number of segments equals [n2/4],[n^2/4], and a connected triangle exists. Prove that any point from which the maximal number of segments starts is a vertex of a connected triangle.