A Note on Even Cycles and Quasirandom Tournaments
نویسندگان
چکیده
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 paper, 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 quasi-random. This resolves an open question raised in 1991 by Chung and Graham [5].
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عنوان ژورنال:
- Journal of Graph Theory
دوره 73 شماره
صفحات -
تاریخ انتشار 2013