The ACO Seminar (2016–2017)

We prove a conjecture of Verstraëte that for r≥3, any r-uniform hypergraph with average degree Ω(k^r-1) contains Berge cycles of k consecutive lengths, which is sharp up to the constant factor. This also leads to some improvements on the Turán numbers of Berge cycles in r-uniform hypergraphs as well as the Zarankiewicz numbers of even cycles. Joint work with T. Jiang