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Infinite dimensional finitely forcible graphon
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Glebov, Roman, Klimošová, Tereza and Králʼ, Daniel (2019) Infinite dimensional finitely forcible graphon. Proceedings of the London Mathematical Society, 118 (4). pp. 826-856. doi:10.1112/plms.12203 ISSN 0024-6115 .
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Official URL: https://doi.org/10.1112/plms.12203
Abstract
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, that is, those determined by finitely many subgraph densities, are of particular interest because of their relation to various problems in extremal combinatorics and theoretical computer science. Lovász and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon always has finite dimension, which would have implications on the minimum number of parts in its weak ε ‐regular partition. We disprove the conjecture by constructing a finitely forcible graphon with the space of typical vertices that has infinite dimension.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Graph theory, Combinatorial analysis | |||||||||||||||
| Journal or Publication Title: | Proceedings of the London Mathematical Society | |||||||||||||||
| Publisher: | Cambridge University Press | |||||||||||||||
| ISSN: | 0024-6115 | |||||||||||||||
| Official Date: | April 2019 | |||||||||||||||
| Dates: |
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| Volume: | 118 | |||||||||||||||
| Number: | 4 | |||||||||||||||
| Page Range: | pp. 826-856 | |||||||||||||||
| DOI: | 10.1112/plms.12203 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Reuse Statement (publisher, data, author rights): | This is the accepted version of the following article: Glebov, R. , Klimošová, T. and Král', D. (2018), Infinite‐dimensional finitely forcible graphon. Proc. London Math. Soc.. . doi:10.1112/plms.12203, which has been published in final form at https://doi.org/10.1112/plms.12203 | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Date of first compliant deposit: | 24 September 2018 | |||||||||||||||
| Date of first compliant Open Access: | 5 November 2018 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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