4 problems

Let $\mathcal{P}^k_n$ and $\mathcal{C}^k_n$ denote the $k$-uniform loose path and loose cycle with $n$ edges, respectively, and let $R(H_1,H_2)$ be the two-colour Ramsey number for…

There exists an integer $n_0$ such that for all $n\geq n_0$, the following holds. Let $\mathcal{C}$ be a $3$-graph consisting of vertex-disjoint loose cycles…

Loose-cycle factor conjecture. If $n$ is sufficiently large and

Let $\mathcal{C}^k_n$ denote the $k$-uniform loose cycle with $n$ edges, and let $R(\mathcal{H},\mathcal{G})$ be the Ramsey number for hypergraphs $\mathcal{H}$ and $\mathcal{G}$.…