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Bibliographic Details
Main Authors: Grzesik, Andrzej, Kráľ, Daniel, Mohr, Samuel
Format: Preprint
Published: 2021
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Online Access:https://arxiv.org/abs/2103.10354
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author Grzesik, Andrzej
Kráľ, Daniel
Mohr, Samuel
author_facet Grzesik, Andrzej
Kráľ, Daniel
Mohr, Samuel
contents The notion of first order convergence of graphs unifies the notions of convergence for sparse and dense graphs. Nešetřil and Ossona de Mendez [J. Symbolic Logic 84 (2019), 452-472] proved that every first order convergent sequence of graphs from a nowhere-dense class of graphs has a modeling limit and conjectured the existence of such modeling limits with an additional property, the strong finitary mass transport principle. The existence of modeling limits satisfying the strong finitary mass transport principle was proved for first order convergent sequences of trees by Nešetřil and Ossona de Mendez [Electron. J. Combin. 23 (2016), P2.52] and for first order sequences of graphs with bounded path-width by Gajarský et al. [Random Structures Algorithms 50 (2017), 612-635]. We establish the existence of modeling limits satisfying the strong finitary mass transport principle for first order convergent sequences of graphs with bounded tree-width.
format Preprint
id arxiv_https___arxiv_org_abs_2103_10354
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Strong modeling limits of graphs with bounded tree-width
Grzesik, Andrzej
Kráľ, Daniel
Mohr, Samuel
Combinatorics
The notion of first order convergence of graphs unifies the notions of convergence for sparse and dense graphs. Nešetřil and Ossona de Mendez [J. Symbolic Logic 84 (2019), 452-472] proved that every first order convergent sequence of graphs from a nowhere-dense class of graphs has a modeling limit and conjectured the existence of such modeling limits with an additional property, the strong finitary mass transport principle. The existence of modeling limits satisfying the strong finitary mass transport principle was proved for first order convergent sequences of trees by Nešetřil and Ossona de Mendez [Electron. J. Combin. 23 (2016), P2.52] and for first order sequences of graphs with bounded path-width by Gajarský et al. [Random Structures Algorithms 50 (2017), 612-635]. We establish the existence of modeling limits satisfying the strong finitary mass transport principle for first order convergent sequences of graphs with bounded tree-width.
title Strong modeling limits of graphs with bounded tree-width
topic Combinatorics
url https://arxiv.org/abs/2103.10354