3 problems

Let $S'$ be a finite set of graphs, and let $\operatorname{Forb}_\subseteq(S')$ denote the graphs containing no member of $S'$ as an induced subgraph. Many-forbidden-graphs conject…

Let $H$ be a graph, let $S$ be a finite set of graphs, and write $\operatorname{Forb}_\subseteq(S)$ for the graphs containing no member of $S$ as an induced subgraph. One-forbidden…

Let $(\mathcal{F},\le)$ be a well-quasi-order (wqo), and suppose there are algorithms for basic problems related to $\le$, including deciding whether $X\le Y$ and, given $X$, findi…