6 problems

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…

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,

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…