Treeable Graphings Are Local Limits of Finite Graphs

2016/01/21 by Hosseini, Lucas, de Mendez, Patrice Ossona
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.05580

Abstract

Let \mathbf G be a graphing, that is a Borel graph defined by d measure preserving involutions. We prove that if \mathbf G is \em treeable then it arises as the local limit of some sequence (G_n)_n∈ℕ of graphs with maximum degree at most d. This extends a result by Elek [G. Elek, Note on limits of finite graphs, Combinatorica 27 (2007)] (for \mathbf G a treeing) and consequently extends the domain of the graphings for which Aldous-Lyons conjecture is known to be true.

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