5 problems

Duffus–Goddard–Rödl conjecture. Most graph classes characterized by a 2-connected pattern are NP-complete to recognize.

Let $\mathcal{F}$ consist of a single 2-connected forbidden pattern other than a complete graph, and let $\operatorname{Ord}(\mathcal{F})$ denote the problem of deciding whether an…

Let $\mathcal{F}$ be a set of forbidden patterns, and let $\operatorname{Ord}(\mathcal{F})$ denote the problem of deciding whether an input graph admits an ordering avoiding every…

Nonlinear containment conjecture. Every nonlinear sequence $\sigma$ contains $ababa$, $abcacbc$, or some sequence morally equivalent to $abcacbc$.

Doubling conjecture. In general, it is not true that