A Note on Even Cycles and Quasirandom Tournaments. Issue 3 (15th June 2012) - Kalyanasundaram, Subrahmanyam
Abstract A cycle C={v1, v2, ..., v1} in a tournament T is said to be even, if when walking along C, an even number of edges point in the wrong direction, that is, they are directed from vi+1 to vi. In this short article, we show that for every fixed even integer k≥4, if close to half of the k‐cycles in a tournament T are even, then T must be quasirandom.This resolves an open question raised in 1991 by Chung and Graham 1991.