A Note on Even Cycles and Quasi-Random Tournaments
Combinatorics
2012-06-19 v2
Abstract
A cycle C={v_1,v_2,....,v_1} 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 v_{i+1} to v_i. 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
Cite
@article{arxiv.1108.0011,
title = {A Note on Even Cycles and Quasi-Random Tournaments},
author = {Subrahmanyam Kalyanasundaram and Asaf Shapira},
journal= {arXiv preprint arXiv:1108.0011},
year = {2012}
}