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arXiv · 2009.01985

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

Natasha Dobrinen
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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.

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Natasha Dobrinen. 2020-09-04. The Ramsey theory of the universal homogeneous triangle-free graph Part II: Exact big Ramsey degrees. https://arxiv.org/abs/2009.01985

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