EPPA for reducts of the random graph

Classify which reducts of the random graph have EPPA and coherent EPPA.

Background

The random graph and the empty structure are settled, while two-graphs have EPPA but unresolved coherence, and the complementing graph and complementing two-graph remain unresolved for both properties.

References

Which of the reducts of the random graph have (coherent) EPPA?

— Twenty years of Nešetřil's classification programme of Ramsey classes  (2501.17293 - Hubička et al., 28 Jan 2025) in Question, subsection EPPA