Kalyanasundaram, Subrahmanyam and Shapira, A
(2013)
A Note on Even Cycles and QuasiRandom Tournaments.
Journal of Graph Theory, 73.
pp. 260266.
ISSN 03649024
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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.
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