Treeable Graphings are Local Limits of Finite Graphs

Lucas Hosseini (1) , Patrice Ossona de Mendez (2, 1)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 IUUK - Computer Science Institute of Charles University [Prague]

Let G be a graphing, that is a Borel graph defined by d measure preserving involutions. We prove that if G is treeable then it arises as the local limit of some sequence (Gn) of graphs with maximum degree at most d. This extends a result by Elek (for G a treeing) and consequently extends the domain of the graphings for which Aldous–Lyons conjecture is known to be true.

Mots clés: graph limit; local convergence; graphing; treeing

Domaines: Combinatoire [math.CO]

Lucas Hosseini, Patrice Ossona de Mendez. Treeable Graphings are Local Limits of Finite Graphs. 2016. ⟨hal-01252409⟩