The tournament involves $2k$ tennis players they play the tournament, each played with each exactly once. What is the minimum number of rounds you need to play to find 3 such that everyone plays with everyone?
In each round, $k$ games are played. I proved that if $k ^ 2 + 1$ edges will be drawn in a graph of $2k$ vertices, then a triangle is sure to exist, that is, if $k + 1$ round is held. And how to prove that $k$ rounds is not enough, I did not understand, I predict that this is proved by induction.