On the maximum size of connected hypergraphs without a path of given length

Ervin Győri, Abhishek Methuku, Nika Salia, Casey Tompkins, Máté Vizer

Published 2017-10-23Version 1

In this note we asymptotically determine the maximum number of hyperedges possible in an $r$-uniform, connected $n$-vertex hypergraph without a Berge path of length $k$, as $n$ and $k$ tend to infinity. We show that, unlike in the graph case, the multiplicative constant is smaller with the assumption of connectivity.