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Compactness and finite forcibility of graphons
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Glebov, Roman, Králʼ, Daniel and Volec, Jan (2019) Compactness and finite forcibility of graphons. Journal of the European Mathematical Society, 21 (10). pp. 3199-3223. doi:10.4171/JEMS/901 ISSN 1435-9855.
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Official URL: https://doi.org/10.4171/JEMS/901
Abstract
Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are referred to as finitely forcible. Following the intuition that such graphons should have finitary structure, Lovasz and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon is always compact. We disprove the conjecture by constructing a finitely forcible graphon such that the associated space is not compact. The construction method gives a general framework for constructing finitely forcible graphons with non-trivial properties.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science) | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Combinatorial analysis, Graph theory | |||||||||||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | |||||||||||||||
| Publisher: | European Mathematical Society Publishing House | |||||||||||||||
| ISSN: | 1435-9855 | |||||||||||||||
| Official Date: | 24 June 2019 | |||||||||||||||
| Dates: |
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| Volume: | 21 | |||||||||||||||
| Number: | 10 | |||||||||||||||
| Page Range: | pp. 3199-3223 | |||||||||||||||
| DOI: | 10.4171/JEMS/901 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Copyright Holders: | © 2019. European Mathematical Society | |||||||||||||||
| Date of first compliant deposit: | 29 April 2019 | |||||||||||||||
| Date of first compliant Open Access: | 30 April 2019 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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