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Automorphism groups and Ramsey properties of sparse graphs
File | Description | Size | Format | |
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SparseRamsey-final.pdf | Accepted version | 488.02 kB | Adobe PDF | View/Open |
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 |