Weak regularity and finitely forcible graph limits
| dc.contributor.author | Cooper, Jacob W. | |
| dc.contributor.author | Kaiser, Tomáš | |
| dc.contributor.author | Král', Daniel | |
| dc.contributor.author | Noel, Jonathan A. | |
| dc.date.accessioned | 2019-10-28T11:00:12Z | |
| dc.date.available | 2019-10-28T11:00:12Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract-translated | Graphons are analytic objects representing limits of convergent sequences of graphs. Lovász and Szegedy conjectured that every finitely forcible graphon, i.e. any graphon determined by finitely many subgraph densities, has a simple structure. In particular, one of their conjectures would imply that every finitely forcible graphon has a weak ε-regular partition with the number of parts bounded by a polynomial in ε^{−1}. We construct a finitely forcible graphon W such that the number of parts in any weak ε-regular partition of W is at least exponential in ε^{−2}/2^{5 log* ε^{-2}}. This bound almost matches the known upper bound for graphs and, in a certain sense, is the best possible for graphons. | en |
| dc.format | 32 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | COOPER, J. W., KAISER, T., KRÁL', D., NOEL, J. A. Weak regularity and finitely forcible graph limits. Transactions of the American mathematical society, 2018, roč. 370, č. 6, s. 3833-3864. ISSN 0002-9947. | en |
| dc.identifier.document-number | 428311400003 | |
| dc.identifier.doi | 10.1090/tran/7066 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.obd | 43927060 | |
| dc.identifier.uri | 2-s2.0-85044404667 | |
| dc.identifier.uri | http://hdl.handle.net/11025/35700 | |
| dc.language.iso | en | en |
| dc.project.ID | GA14-19503S/Barevnost a struktura grafů | cs |
| dc.publisher | American Mathematical Society | en |
| dc.relation.ispartofseries | Transactions Of The American Mathematical Society | en |
| dc.rights | Plný text není přístupný. | cs |
| dc.rights | © American Mathematical Society | en |
| dc.rights.access | closedAccess | en |
| dc.subject.translated | graph limit | en |
| dc.subject.translated | graphon | en |
| dc.subject.translated | weak regularity | en |
| dc.subject.translated | forcibility | en |
| dc.title | Weak regularity and finitely forcible graph limits | en |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |