Hypergraphs with Few Berge Paths of Fixed Length between Vertices
Hypergraphs with Few Berge Paths of Fixed Length between Vertices
In this paper we study the maximum number of hyperedges which may be in an $r$-uniform hypergraph under the restriction that no pair of vertices has more than $t$ Berge paths of length $k$ between them. When $r=t=2$, this is the even-cycle problem asking for ${ex}(n, C_{2k})$. We extend results …