3 problems

Let a graph or digraph property be monotone if it is preserved under deletion of edges or arcs, and let a property be non-trivial if it is neither always true nor always false. A p…

Let a graph property be a partition of the unlabeled graphs on a fixed number of vertices into graphs with and without the property. The property is monotone if it is preserved und…

Let $E$ be a finite ground set, let $\mathcal{F}\subseteq 2^E$ be a set system, and let $G\subseteq \operatorname{Symm}_E$ be a symmetry group acting transitively on $E$. Assume th…