5 problems

Nash-Williams' conjecture. If

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

Yuster's triangle-decomposition conjecture. If $d\gg\sqrt{n\log n}$ and $d$ is even, then asymptotically almost surely $G_{n,d}$ has a $K_3$-decomposition provided $3\mid dn$.

High-girth Nash-Williams conjecture. For every fixed $g$, every sufficiently large $K_3$-divisible graph $G$ with

Let $G$ be a graph with $n$ vertices and minimum degree at least $\frac{3}{4}n$. Garaschuk's conjecture. If $n$ is large enough, then $G$ is fractionally $K_3$-decomposable. Fracti…