This work was done while being a student in School of Computer Science, Georgia Institute of Technology, Atlanta, GA 30332.
A Note on Even Cycles and Quasirandom Tournaments
Article first published online: 15 JUN 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 73, Issue 3, pages 260–266, July 2013
How to Cite
Kalyanasundaram, S. and Shapira, A. (2013), A Note on Even Cycles and Quasirandom Tournaments. J. Graph Theory, 73: 260–266. doi: 10.1002/jgt.21671
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.
- Issue published online: 10 MAY 2013
- Article first published online: 15 JUN 2012
- Manuscript Revised: 12 APR 2012
- Manuscript Received: 29 JUL 2011
- NSF. Grant Number: DMS-0901355
- ISF. Grant Number: 224/11
- Marie-Curie CIG. Grant Number: 303320
A cycle 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 to . In this short article, we show that for every fixed even integer , 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.