Submission date: 3 January 2018

Abstract:

We study automorphism groups of sparse graphs from the viewpoint of topological dynamics and the Kechris, Pestov, Todorčević correspondence. We investigate amenable and extremely amenable subgroups of these groups using the space of orientations of the graph and results from structural Ramsey theory. Resolving one of the open questions in the area, we show that Hrushovski's example of an ω-categorical sparse graph has no ω-categorical expansion with extremely amenable automorphism group.

Mathematics Subject Classification: Primary 05D10, 20B27, 37B05, Secondary 03C15, 05C55, 22F50, 54H20

Keywords and phrases:

Full text arXiv 1801.01165: pdf, ps.