4 problems

Piecewise asymptotic conjecture for random 3-uniform linear 4-cycles.

Let $G_{n,p}^{(3)}$ be the random 3-uniform hypergraph on $n$ vertices, let $C_4^{(3)}$ be the 3-uniform expansion of the 4-cycle, and let…

Let $r$ be a positive integer and let $\mathcal H$ be an $r$-uniform hypergraph on $n$ vertices with no cycle of length $r$ or longer. The extremal bound conjecture. Then … This co…

Let $f_k(n)$ denote the maximum number of edges in an $n$-vertex $k$-uniform hypergraph containing no generalized $4$-cycle. For $k\geq 4$ and $n\in\mathbb{N}$, Füredi's conjecture…