## Ruth Luo gave a talk on the induced Turán-type problems for hypergraphs at the discrete math seminar

On November 19, 2019, Ruth Luo from University of California San Diego gave a talk on the Turán-type results on r-uniform hypergraphs without a certain structure called an induced Berge-F. The title of her talk was “Induced Turán problems for hypergraphs“. She is visiting IBS discrete mathematics group until November 22.

## Ruth Luo, Induced Turán problems for hypergraphs

Let $F$ be a graph. We say that a hypergraph $\mathcal H$ is an induced Berge $F$ if there exists a bijective mapping $f$ from the edges of $F$ to the hyperedges of $\mathcal H$ such that for all $xy \in E(F)$, $f(xy) \cap V(F) = \{x,y\}$. In this talk, we show asymptotics for the maximum number of edges in $r$-uniform hypergraphs with no induced Berge $F$. In particular, this function is strongly related to the generalized Turán function $ex(n,K_r, F)$, i.e., the maximum number of cliques of size $r$ in $n$-vertex, $F$-free graphs.  Joint work with Zoltan Füredi.

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209