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Finitely forcible graphons with an almost arbitrary structure
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Králʼ, Daniel, Lovasz, Laszlo M., Noel, Jonathan A. and Sosnovec, Jakub (2020) Finitely forcible graphons with an almost arbitrary structure. Discrete Analysis . doi:10.19086/da.12058 ISSN 2397-3129.
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Official URL: https://doi.org/10.19086/da.12058
Abstract
Graphons are analytic objects representing convergent sequences of large graphs. A graphon is said to be finitely forcible if it is determined by finitely many subgraph densities, i.e., if the asymptotic structure of graphs represented by such a graphon depends only on finitely many density constraints. Such graphons appear in various scenarios, particularly in extremal combinatorics.
Lovasz and Szegedy conjectured that all finitely forcible graphons possess a simple structure. This was disproved in a strong sense by Cooper, Kral and Martins, who showed that any graphon is a subgraphon of a finitely forcible graphon. We strenghten this result by showing for every ε>0 that any graphon spans a 1−ε proportion of a finitely forcible graphon.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Extremal problems (Mathematics) , Combinatorial analysis | ||||||||||||||||||
| Journal or Publication Title: | Discrete Analysis | ||||||||||||||||||
| Publisher: | Diamond Open Access Journals | ||||||||||||||||||
| ISSN: | 2397-3129 | ||||||||||||||||||
| Official Date: | 31 July 2020 | ||||||||||||||||||
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| DOI: | 10.19086/da.12058 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
| Date of first compliant deposit: | 10 March 2020 | ||||||||||||||||||
| Date of first compliant Open Access: | 16 March 2020 | ||||||||||||||||||
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