11 problems

For a complete graph $K_r$, let $M_{K_r}(n)$ be the maximum running time of the $K_r$-bootstrap percolation process over all graphs on $n$ vertices. Bollobás–Przykucki–Riordan–Saha…

Let $\ell$ be the cycle length, and consider the random graph process that begins with the empty graph and adds uniformly random edges while maintaining the condition that no copy…

Let $n$ be the number of vertices, let $[M]$ denote the set of admissible times, let $t$ be a time parameter, and let $b$ be a budget parameter. A $(t,b)$-strategy is a strategy in…

Multi-nest convergence conjecture. The multi-nest ant process converges on any underlying graph, although the limiting behavior is not specified.

Hitting-time conjecture. W.h.p., for every $t \geq \tau$, $G_t$ admits an FTD.

Non-central-factor conjecture. Let $H$ be a fixed non-central graph. Then, for every strategy $\sigma\in\operatorname{\mathcal{S}}_n$,

Minimum-degree construction-time conjecture. The conclusion of Theorem holds for $k=o(n)$.

Degeneracy-order conjecture. With high probability,

Let $H$ be a strictly balanced graph, meaning that for every proper subgraph $F\subsetneq H$, … Define … For the $H$-free random graph process, let $G_{n,H}$ denote its final graph…

Blue-edge density conjecture. As $n\to\infty$,

Dense fixed-subgraph conjecture. With high probability, the final graph of the $H$-free process contains no copy of $F$. This strengthens the proved result for graphs whose number…