There exist four mathematicians - ILL 1990 FRA3
Source:
September 18, 2010
combinatoricsgraph theoryExtremal Graph TheoryClique numberIMO ShortlistIMO Longlist
Problem Statement
1990 mathematicians attend a meeting, every mathematician has at least 1327 friends (the relation of friend is reciprocal). Prove that there exist four mathematicians among them such that any two of them are friends.