Modeling limits in hereditary classes: Reduction and application to trees

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333127" target="_blank" >RIV/00216208:11320/16:10333127 - isvavai.cz</a>
Result on the web
<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p52" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p52</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Modeling limits in hereditary classes: Reduction and application to trees
Original language description
The study of limits of graphs led to elegant limit structures for sparse and dense graphs. This has been unified and generalized by the authors in a more general setting combining analytic tools and model theory to FO-limits (and X-limits) and to the notion of modeling. The existence of modeling limits was established for sequences in a bounded degree class and, in addition, to the case of classes of trees with bounded height and of graphs with bounded tree depth. The natural obstacle for the existence of modeling limit for a monotone class of graphs is the nowhere dense property and it has been conjectured that this is a sufficient condition. Extending earlier results here we derive several general results which present a realistic approach to this conjecture. As an example we then prove that the class of all finite trees admits modeling limits.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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