4 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

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

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