A counterexample to the Bollobás–Riordan conjectures on sparse graph limits

Sah, Ashwin; Sawhney, Mehtaab; Tidor, Jonathan; Zhao, Yufei

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dc.contributor.author	Sah, Ashwin
dc.contributor.author	Sawhney, Mehtaab
dc.contributor.author	Tidor, Jonathan
dc.contributor.author	Zhao, Yufei
dc.date.accessioned	2021-10-27T19:57:39Z
dc.date.available	2021-10-27T19:57:39Z
dc.date.issued	2021
dc.identifier.uri	https://hdl.handle.net/1721.1/134018
dc.description.abstract	© The Author(s), 2021. Published by Cambridge University Press. Bollobás and Riordan, in their paper 'Metrics for sparse graphs', proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to sparse graphs. We refute these conjectures by exhibiting a sequence of graphs with convergent normalized subgraph densities (and pseudorandom C4-counts), but with no limit expressible as a kernel.
dc.language.iso	en
dc.publisher	Cambridge University Press (CUP)
dc.relation.isversionof	10.1017/S0963548321000031
dc.rights	Creative Commons Attribution-Noncommercial-Share Alike
dc.rights.uri	http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.source	arXiv
dc.title	A counterexample to the Bollobás–Riordan conjectures on sparse graph limits
dc.type	Article
dc.relation.journal	Combinatorics Probability and Computing
dc.eprint.version	Original manuscript
dc.type.uri	http://purl.org/eprint/type/JournalArticle
eprint.status	http://purl.org/eprint/status/NonPeerReviewed
dc.date.updated	2021-06-01T18:06:59Z
dspace.orderedauthors	Sah, A; Sawhney, M; Tidor, J; Zhao, Y
dspace.date.submission	2021-06-01T18:07:00Z
mit.journal.volume	30
mit.journal.issue	5
mit.license	OPEN_ACCESS_POLICY
mit.metadata.status	Authority Work and Publication Information Needed