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Automorphism groups and Ramsey properties of sparse graphs

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Title: Automorphism groups and Ramsey properties of sparse graphs
Authors: Evans, DM
Hubička, J
Nešetřil, J
Item Type: Journal Article
Abstract: We study automorphism groups of sparse graphs from the viewpoint of topological dynamics and the Kechris, Pestov, Todor\v{c}evi\'c 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.
Issue Date: 1-Aug-2019
Date of Acceptance: 21-Feb-2019
URI: http://hdl.handle.net/10044/1/67998
DOI: https://dx.doi.org/10.1112/plms.12238
ISSN: 1460-244X
Publisher: London Mathematical Society
Start Page: 515
End Page: 546
Journal / Book Title: Proceedings of the London Mathematical Society
Volume: 119
Issue: 2
Copyright Statement: © 2019 London Mathematical Society. This is the accepted version of the following article: Evans, D. M., Hubička, J. and Nešetřil, J. (2019), Automorphism groups and Ramsey properties of sparse graphs. Proc. London Math. Soc.. doi:10.1112/plms.12238, which has been published in final form at https://dx.doi.org/10.1112/plms.12238
Keywords: math.GR
math.GR
cs.DM
math.CO
math.DS
math.LO
05D10, 20B27, 37B05 (Primary), 03C15, 05C55, 22F50, 54H20 (Secondary)
G.2.2; F.4.1
math.GR
math.GR
cs.DM
math.CO
math.DS
math.LO
05D10, 20B27, 37B05 (Primary), 03C15, 05C55, 22F50, 54H20 (Secondary)
G.2.2; F.4.1
0101 Pure Mathematics
Notes: 41 pages, 2 figures, minor revision
Publication Status: Published
Online Publication Date: 2019-03-06
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics