First order convergence and roots
Combinatorics
2019-02-20 v1 Discrete Mathematics
Abstract
Nesetril and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if G_i is a sequence of graphs with M being their first order limit and v is a vertex of M, then there exists a sequence v_i of vertices such that the graphs G_i rooted at v_i converge to M rooted at v. We show that this holds for almost all vertices v of M and we give an example showing that the statement need not hold for all vertices.
Keywords
Cite
@article{arxiv.1403.3049,
title = {First order convergence and roots},
author = {Demetres Christofides and Daniel Kral},
journal= {arXiv preprint arXiv:1403.3049},
year = {2019}
}