5 problems

EPPA–Ramsey expansion conjecture. Every strong amalgamation class with EPPA has a precompact Ramsey expansion.

Quadratic EPPA conjecture. The graph $G$ is either a subgraph of a finite homogeneous graph, or every EPPA-witness of $G$ has at least

Random-graph EPPA conjecture. The almost-quadratic lower bound for $G(n,1/2)$ is far from optimal.

Cycle EPPA conjecture. If $n\geq 7$, then

EPPA–Ramsey expansion conjecture. Every class with EPPA has a precompact Ramsey expansion.