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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 1, Pages 139–160 (Mi izv8317)  

Big subsets with small boundaries in a graph with a vertex-transitive group of automorphisms

N. Seiftera, V. I. Trofimovbc

a Montanuniversität Leoben, Austria
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
c Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: The theory of ends of finitely generated groups $G$ and connected locally finite graphs $\Gamma$ with vertex-transitive groups of automorphisms can be regarded as a theory of Boolean algebras of subsets of $G$ or vertex set of $\Gamma$ with finite boundaries (in the locally finite Cayley graph of $G$ or in $\Gamma$ respectively), considered modulo finite subsets. We develop a more general theory where infinite subsets with finite boundaries are replaced by certain ‘big’ subsets with ‘small’ boundaries.

Keywords: group, graph, vertex-transitive group of automorphisms, end.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00349
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Supported in part by RFBR grant no. 10-01-00349 and by the Programme of State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of 27.08.2013).


DOI: https://doi.org/10.4213/im8317

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English version:
Izvestiya: Mathematics, 2017, 81:1, 137–155

Bibliographic databases:

UDC: 512.54+519.17
MSC: 05C25, 20F65, 20F69
Received: 07.11.2014
Revised: 12.01.2016

Citation: N. Seifter, V. I. Trofimov, “Big subsets with small boundaries in a graph with a vertex-transitive group of automorphisms”, Izv. RAN. Ser. Mat., 81:1 (2017), 139–160; Izv. Math., 81:1 (2017), 137–155

Citation in format AMSBIB
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