5 problems

Vertex-minor universality conjecture. If

Let $D$ be a positive integer, let $\mathcal{H}(n,D)$ be the class of all $n$-vertex $D$-degenerate graphs, and let an $\mathcal{H}(n,D)$-universal graph be a graph containing ever…

Folklore universality conjecture. For every $\Delta\geq 3$, this lower bound gives the correct order of magnitude for the threshold probability of $G(n,p)$ to be…

Universality conjecture. Asymptotically almost surely, $G_\alpha\cup G(n,p)$ is $\mathcal{F}(n,\Delta)$-universal, meaning that it contains every $n$-vertex graph of maximum degree…

Let $K_n$ be the complete graph. For positive integers $r$ and $\Delta$, and a constant $\beta>0$, let $\mathcal{H}_r^{\beta n}(n,\Delta)$ denote the class of graphs relevant to th…