Automorphism groups and Ramsey properties of sparse graphs

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 $\omega$-categorical sparse graph has no $\omega$-categorical expansion with extremely amenable automorphism group.

41 pages, 2 figures, minor revision

References in corpus (2)

• Universal minimal flows of generalized Ważewski dendrites
• Consistent random vertex-orderings of graphs

Cited by in corpus (6)

• All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
• Ramsey expansions of metrically homogeneous graphs
• Cores over Ramsey structures
• Forbidden cycles in metrically homogeneous graphs
• Sparse graphs and the fixed points on type spaces property
• Twenty years of Nešetřil's classification programme of Ramsey classes