Connected Hypergraphs without long Berge paths

Abstract

We generalize a result of Balister, Gy{ő}ri, Lehel and Schelp for hypergraphs. We determine the unique extremal structure of an $n$-vertex, $r$-uniform, connected, hypergraph with the maximum number of hyperedges, without a $k$-Berge-path, where $n\ge N_{k,r}$, $k\ge 2r+13>17$.

arXiv comment11 pages, 1 figure