The Ramsey theory of the universal homogeneous triangle-free graph Part II: Exact big Ramsey degrees

Abstract

Building on previous work of the author, for each finite triangle-free graph $\mathbf{G}$, we determine the equivalence relation on the copies of $\mathbf{G}$ inside the universal homogeneous triangle-free graph, ${\mathcal{H}}_3$, with the smallest number of equivalence classes so that each one of the classes persists in every isomorphic subcopy of ${\mathcal{H}}_3$. This characterizes the exact big Ramsey degrees of ${\mathcal{H}}_3$. It follows that the triangle-free Henson graph is a big Ramsey structure.

22 pages

References in corpus (1)

• A Categorical Notion of Precompact Expansion