On the limit of large girth graph sequences

Abstract

Let d≥2 be given and let µ be an involution-invariant probability measure on the space of trees TT d with maximum degrees at most d. Then µ arises as the local limit of some sequence {G n } n=1 of graphs with all degrees at most d. This answers Question 3.3 of Bollobás and Riordan [4].

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Correspondence to Gábor Elek.

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Elek, G. On the limit of large girth graph sequences. Combinatorica 30, 553–563 (2010). https://doi.org/10.1007/s00493-010-2559-2

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Mathematics Subject Classification (2000)

  • 05C99