Topological Graph Theory

Abstract

2. (Iran Team Selection Test 2008/6) Suppose 799 teams participate in a tournament in which every pair of teams plays against each other exactly once. Prove that there exist two disjoint groups A and B of 7 teams each such that every team from A defeated every team from B. Solution: SampleA as a random 7-set. LetX be the number of guys that are totally dominated byA. Letting dv denote the in-degree of v, we have E [X] = ∑