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Limits of locally–globally convergent graph sequences

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Abstract

The colored neighborhood metric for sparse graphs was introduced by Bollobás and Riordan [BR11]. The corresponding convergence notion refines a convergence notion introduced by Benjamini and Schramm [BS01]. We prove that even in this refined sense, the limit of a convergent graph sequence (with uniformly bounded degree) can be represented by a graphing. We study various topics related to this convergence notion such as: Bernoulli graphings, factor of i.i.d. processes and hyperfiniteness.

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Authors and Affiliations

  1. School of Computer Science, McGill University, Montreal, QC, H3A 0G4, Canada

    Hamed Hatami

  2. Institute of Mathematics, Eötvös Loránd University, Budapest, 1117, Hungary

    László Lovász

  3. Department of Mathematics, University of Toronto, Toronto, ON, M5S2E4, Canada

    Balázs Szegedy

Authors
  1. Hamed Hatami
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  2. László Lovász
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  3. Balázs Szegedy
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Corresponding author

Correspondence to László Lovász.

Additional information

Research of H.H. was supported by an NSERC and an FQRNT grant. Research of L.L. was supported by ERC Grant No. 227701 and OTKA grant No. CNK 77780. Research of B.Sz. was supported by an NSERC grant.

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Hatami, H., Lovász, L. & Szegedy, B. Limits of locally–globally convergent graph sequences. Geom. Funct. Anal. 24, 269–296 (2014). https://doi.org/10.1007/s00039-014-0258-7

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  • DOI: https://doi.org/10.1007/s00039-014-0258-7

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