Aug. 25, 3:30pm, Wean 7218 (Note unusual day and location)

Jie Ma, University of Science and Technology of China

Berge cycles of consecutive lengths

Jie Ma, University of Science and Technology of China

Berge cycles of consecutive lengths

Abstract:

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