# Conjugacy for homogeneous ordered graphs

This post is a link to https://arxiv.org/abs/1804.04609

With Paul Ellis. *Archive for mathematical logic*, 2019. (ordered graphs in journal)

*Abstract*: We show that for any countable homogeneous ordered graph $G$, the conjugacy problem for automorphisms of $G$ is Borel complete. In fact we establish that each such $G$ satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of $G$ is Borel reducible to the conjugacy relation on automorphisms of $G$.