A Note on Even Cycles and Quasirandom Tournaments


  • This work was done while being a student in School of Computer Science, Georgia Institute of Technology, Atlanta, GA 30332.

  • Contract grant sponsor: NSF; Contract grant number: DMS-0901355; Contract grant sponsor: ISF; Contract grant number: 224/11; Contract grant sponsor: Marie-Curie CIG; Contract grant number: 303320.


A cycle math formula 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 math formula to math formula. In this short article, we show that for every fixed even integer math formula, 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.