Christofides, Demetres and Králʼ, Daniel (2016) First order convergence and roots. Combinatorics, Probability and Computing, 25 (2). pp. 213-221. doi:10.1017/S0963548315000048 ISSN 0963-5483.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Convergence
Journal or Publication Title:	Combinatorics, Probability and Computing
Publisher:	Cambridge University Press
ISSN:	0963-5483
Official Date:	March 2016
Dates:	Date Event March 2016 Published 24 February 2014 Available 14 March 2014 Submitted
Volume:	25
Number:	2
Number of Pages:	10
Page Range:	pp. 213-221
DOI:	10.1017/S0963548315000048
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	4 March 2016
Date of first compliant Open Access:	4 March 2016
Funder:	European Research Council (ERC), Seventh Framework Programme (European Commission) (FP7)
Grant number:	259385 (ERC)

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