Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphism groups and Ramsey properties of sparse graphs   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.

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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: math-ph