Ramsey expansions of large-girth graph classes

Determine for which integers g≥5 the functional expansion of the class of finite graphs of girth at least g has a precompact Ramsey expansion.

Background

For g≥5, finite graphs of girth at least g do not have the amalgamation property in their ordinary graph language. The paper introduces a binary functional expansion encoding short paths to recover amalgamation and asks whether these expanded classes admit precompact Ramsey expansions.

References

For which $g\geq 5$ does $\mathcal C_g+$ have a precompact Ramsey expansion?

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