## Find Berge hypergraphs by looking at the shadow

- April 12, 2019
- 2:30 p.m.
- LeConte 312

## Abstract

We present some recent results about extremal problems on Berge hypergraphs from the perspectives of the shadow graph. In particular, we show that every sufficiently large hypergraph with co-degree 1 (thus its shadow graph is complete) is pancyclic, i.e., it contains Berge cycles of all possible lengths from three to the number of vertices in the hypergraph. We also define two variants of the Ramsey number and the Turan number in hypergraphs, namely the cover Ramsey number and the cover Turan number and show some new results about these variants. Joint work with Linyuan Lu.