Navegando por Assunto "3-cycles"

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    The shifted Turán sieve method on tournaments II.
    (2021) Kuo, Wentang; Liu, Yu-Ru; Ribas, Sávio; Zhou, Kevin
    In 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.