SEMINARS
Codegree Turan density of complete r-uniform hypergraphs.

2019-06-04　15:00 — 17:00

440

Yi Zhao

Georgia State University, USA

Fix an integer r>2. Given an r-uniform hypergraph (r-graph) H, the minimum codegree D(H) is the largest integer
t such that every (r-1)-subset of V(H) is contained in at least t edges of H. Given an r-graph F,  the codegree Turan
density g(F) is the smallest g >0 such that every graph H on n vertices with D(H)\ge (g + o(1))n contains F as a
subhypergraph. Using known results on the independence number of hypergraphs, we show that there are constants
c_1, c_2>0 depending only on r such that 1 - c_2 ln t / t^{r-1} \le g(K_t^r) \le 1 - c_1 ln t / t^{r-1},
where K_t^r is the complete r-graph on t vertices. This gives the best (general) bounds for g(K_t^r).