On Tight Cycles in Hypergraphs
On Tight Cycles in Hypergraphs
A tight $k$-uniform $\ell$-cycle, denoted by $TC_\ell^k$, is a $k$-uniform hypergraph whose vertex set is $v_0, \ldots, v_{\ell-1}$, and the edges are all the $k$-tuples $\{v_i, v_{i+1}, \ldots, v_{i+k-1}\}$, with subscripts modulo $\ell$. Motivated by a classic result in graph theory that every $n$-vertex cycle-free graph has at most $n-1$ …