12 problems

Morris–Wang conjecture. The asymptotic results for $|\mathrm{Forb}(n,C_k^{(r)})|$ obtained for even $k$ and $r=3$ should hold for all $k,r\geq 3$.

For integers $r\geqslant 3$ and $\ell\geqslant 4$, let $\operatorname{Forb}_r^L(n,C_\ell^r)$ denote the family of $n$-vertex linear $r$-uniform hypergraphs containing no linear cyc…

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

Growth-rate conjecture for random 3-uniform linear 4-cycles. For $n^{-1}\leq p\leq n^{-1/2}$, the correct growth rate of $\mathrm{ex}(G_{n,p}^{(3)},C_4^{(3)})$ is $n^{4/3}$.

Let an $r$-graph be an $r$-uniform hypergraph on $n$ vertices, and let a tight cycle of length $\ell$ be the hypergraph formed from $\ell$ cyclically ordered vertices by taking the…

Mubayi–Yepremyan conjecture. With high probability,

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 $G_{n,p}^{(3)}$ 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 $G_{n,p}^{(r)}$ be the random $r$-uniform hypergraph on $n$ vertices, and let $C_{2\ell}^{(r)}$ be the $r$-uniform expansion of the even cycle $C_{2\ell}$. The quantity…

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…

Kostochka–Mubayi–Verstraëte conjecture.