Constructing sparsest $\ell$-hamiltonian saturated $k$-uniform hypergraphs for a wide range of $\ell$

Andrzej Ruciński, Andrzej Żak

Given $k\ge 3$ and $1\le \ell <k$, an $(\ell ,k)$-cycle is one in which consecutive edges, each of size $k$, overlap in exactly $\ell$ vertices. We study the smallest number of edge…