@MISC{Csóka_anundecidability, author = {Endre Csóka}, title = {An undecidability result on limits of sparse graphs}, year = {} }

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Abstract

Given a set B of finite rooted graphs and a radius r as an input, we prove that it is undecidable to determine whether there exists a sequence (Gi) of finite bounded degree graphs such that the rooted r-radius neighbourhood of a random node of Gi is isomorphic to a rooted graph in B with probability tending to 1. Our proof implies a similar result for the case where the sequence (Gi) is replaced by a unimodular random graph. 1