Compactness and finite forcibility of graphons

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113679" target="_blank" >RIV/00216224:14330/19:00113679 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4171/JEMS/901" target="_blank" >http://dx.doi.org/10.4171/JEMS/901</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JEMS/901" target="_blank" >10.4171/JEMS/901</a>

Result language
angličtina
Original language name
Compactness and finite forcibility of graphons
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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