16 problems

Let $H$ be an infection rule with at least three edges, let $M_H(n)$ denote the maximum running time of the $H$-process, and let $\operatorname{ex}(n,H-e)$ be the Turán extremal nu…

Let $H$ be a bipartite graph, let $M_H(n)$ denote the maximum running time of the $H$-process, and let $\operatorname{ex}(n,H)$ be the Turán extremal number of $H$. Bipartite extre…

Let $H$ be an infection rule and let $M_H(n)$ denote its maximum running time. Polynomial-exponent limit conjecture. The limit … exists for every infection rule $H$. The paper does…

Let $K_{3,3}$ be the complete bipartite graph with parts of size three, let $Q_3$ be the three-dimensional cube graph, and let $M_H(n)$ denote the maximum running time of the $H$-p…

Let $H$ be a graph, let ${\mathrm{tw}}(H)$ denote its tree-width, and let $M_H(n)$ denote the maximum running time of the $H$-process. Tree-width two conjecture. Every graph $H$ wi…

Let $H$ be a connected graph and let $u\in V(H)$. Write $H^{u+}$ for the graph obtained from $H$ by attaching a pendant edge at $u$, and let $M_H(n)$ denote the maximum running tim…

Let $H$ be a connected infection rule, and let $M_H(n)$ denote its maximum running time. Sublinear dichotomy conjecture. If … then … The paper describes the classification of conne…

Tree conjecture. For all $t\in\mathbb N$,

Maximum-running-time comparison conjecture. For all infection rules $H$,

Let $H$ be a graph, let ${\mathrm{tw}}(H)$ denote its tree-width, and let $M_H(n)$ denote the maximum running time of the $H$-bootstrap process over all starting graphs on $n$ vert…

Let $H$ be a graph, and let $M_H(n)$ denote the maximum running time of the $H$-bootstrap process over all starting graphs on $n$ vertices. Sublinear running-time conjecture. Every…

For $n\in\mathbb N$, let $M_T(n)$ be the maximum running time of the $T$-bootstrap process over all starting graphs on $n$ vertices. For $t\in\mathbb N$, let $T$ be a tree with $t$…

Let $K_r$ be the complete graph on $r$ vertices, and let $M_{K_r}(n)$ denote the maximum running time of the $K_r$-bootstrap process over all starting graphs on $n$ vertices. Cliqu…

BKPS conjecture.

BPRS conjecture. For every $k\geq 5$,

For $r\geqslant 5$, let $M_r(n)$ denote the maximum number of time steps for which the $K_r$-bootstrap process on $n$ vertices can run before stabilizing. Subquadratic running-time…