Navegando por Autor "Liu, Yu-Ru"

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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.
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    The shifted turán sieve method on tournaments.
    (2019) Kuo, Wentang; Liu, Yu-Ru; Ribas, Sávio; Zhou, Kevin
    We construct a shied version of the Turán sieve method developed by R. Murty and the second author and apply it to counting problems on tournaments. More precisely, we obtain upper bounds for the number of tournaments which contain a ûxed number of restricted r-cycles. hese are the ûrst concrete results which count the number of cycles over “all tournaments”.