5 problems

Resolvable Nash-Williams' conjecture. If $n$ is sufficiently large, $3$ divides $n$, and

Let $n$ be sufficiently large with $n\equiv 3\pmod{6}$, and let $V$ be a common $n$-vertex set. Let $\mathcal{H}=\{H_1,\ldots,H_{n(n-1)/6}\}$ be a collection of $3$-uniform hypergr…

Let $n$ be sufficiently large with $n\equiv 3\pmod{6}$, and let $H$ be a hypergraph on $n$ vertices. A resolvable Steiner triple system is a Steiner triple system whose triples can…

Let $k$ be a positive integer, and consider parallel classes whose blocks are copies of the cycle $C_k$ or the path $P_k$. Cycle-to-path local metamorphosis conjecture. The union o…

Let an $\textbf{STS}(n)$ denote a Steiner triple system of order $n$, and call it resolvable if its triples can be partitioned into perfect matchings. For $n=3\mod 6$, almost-resol…