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.
| Original language | English GB |
|---|---|
| Pages (from-to) | 260-266 |
| Number of pages | 7 |
| Journal | Journal of Graph Theory |
| Volume | 73 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 2013 |
Keywords
- eigenvalues
- quasirandomness
- tournament
ASJC Scopus subject areas
- Geometry and Topology
- Discrete Mathematics and Combinatorics
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