Problem

Source: ELMO Shortlist 2012, C4

Tags: induction, floor function, ceiling function, inequalities, pigeonhole principle, combinatorics proposed, combinatorics



A tournament on $2k$ vertices contains no $7$-cycles. Show that its vertices can be partitioned into two sets, each with size $k$, such that the edges between vertices of the same set do not determine any $3$-cycles. Calvin Deng.