기초과학연구원 이산수학그룹
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.
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.