Kuo, WentangLiu, Yu-RuRibas, SávioZhou, Kevin2023-02-062023-02-062021KUO, W. et al. The shifted Turán sieve method on tournaments II. Discrete Mathematics, v. 344, n. 12, p. 112602, 2021. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0012365X21003150>. Acesso em: 06 jul. 2022.0012-365Xhttp://www.repositorio.ufop.br/jspui/handle/123456789/16121In a previous work [5], we developed the shifted Turán sieve method on a bipartite graph and applied it to problems on cycles in tournaments. More precisely, we obtained upper bounds for the number of tournaments which contain a small number of r-cycles. In this paper, we improve our sieve inequality and apply it to obtain an upper bound for the number of bipartite tournaments which contain a number of 2r-cycles far from the average. We also provide the exact bound for the number of tournaments which contain few 3- cycles, using other combinatorial arguments.en-USrestritoBipartite tournaments3-cyclesArtigo publicado em periodicohttps://www.sciencedirect.com/science/article/pii/S0012365X21003150https://doi.org/10.1016/j.disc.2021.112602