Geodesic
Big subsets with small boundaries in a~graph with a~vertex-transitive group of automorphisms
Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 137-155.

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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: graph, vertex-transitive group of automorphisms, end.
Mots-clés : group 
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N. Seifter; V. I. Trofimov. Big subsets with small boundaries in a~graph with a~vertex-transitive group of automorphisms. Izvestiya. Mathematics , Tome 81 (2017) no. 1, pp. 137-155. http://geodesic.mathdoc.fr/item/IM2_2017_81_1_a4/

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