Strong Modeling Limits of Graphs with Bounded Tree-Width

GRZESIK, Andrzej, Daniel KRÁĽ and Josef Samuel MOHR. Strong Modeling Limits of Graphs with Bounded Tree-Width. In Trends in Mathematics, Volume 14, Extended Abstracts of EuroComb 2021, European Conference on Combinatorics, Graph Theory and Applications. Barcelona: Birkhäuser, 2021, p. 273-279. ISBN 978-3-030-83822-5. Available from: https://dx.doi.org/10.1007/978-3-030-83823-2_43.

Basic information

• Original name: Strong Modeling Limits of Graphs with Bounded Tree-Width
• Authors: GRZESIK, Andrzej (616 Poland), Daniel KRÁĽ (203 Czech Republic, belonging to the institution) and Josef Samuel MOHR (276 Germany, belonging to the institution).
• Edition: Barcelona, Trends in Mathematics, Volume 14, Extended Abstracts of EuroComb 2021, European Conference on Combinatorics, Graph Theory and Applications, p. 273-279, 7 pp. 2021.
• Publisher: Birkhäuser

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: Switzerland
• Confidentiality degree: is not subject to a state or trade secret
• Publication form: printed version "print"
• RIV identification code: RIV/00216224:14330/21:00126000
• Organization unit: Faculty of Informatics
• ISBN: 978-3-030-83822-5
• ISSN: 2297-0215
• Doi: http://dx.doi.org/10.1007/978-3-030-83823-2_43
• Keywords in English: combinatorial limit; first order convergence; graph limit; modeling limit
• Tags: International impact, Reviewed

Abstract

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.