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Insertion-tolerance and repetitiveness of random graphs

Fernando Alcalde Cuesta

Departamento de Matemáticas, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain

GeoDynApp – ECSING Group, Spain

E-mail Address: fernando.alcalde@usc.es

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Álvaro Lozano Rojo

GeoDynApp – ECSING Group, Spain

Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n. E-50090 Zaragoza, Spain

Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Spain

E-mail Address: alvarolozano@unizar.es

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, and

Antón C. Vázquez Martínez

Departamento de Matemáticas, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain

GeoDynApp – ECSING Group, Spain

E-mail Address: anton.vazquez@yahoo.es

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https://doi.org/10.1142/S021949371750023XCited by:0 (Source: Crossref)

Abstract

Bond percolation on Cayley graphs provides examples of random graphs. Other examples arise from the dynamical study of proper repetitive subgraphs of Cayley graphs. In this paper we demonstrate that these two families have mutually singular laws as a corollary of a general lemma about countable Borel equivalence relations on first countable Hausdorff spaces.

Keywords:

AMSC: 05C80, 37A20, 60B05, 60C05

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