Publication details
Strong Modeling Limits of Graphs with Bounded Tree-Width
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Proceedings |
| Conference | Trends in Mathematics, Volume 14, Extended Abstracts of EuroComb 2021, European Conference on Combinatorics, Graph Theory and Applications |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-030-83823-2_43 |
| Keywords | combinatorial limit; first order convergence; graph limit; modeling limit |
| Description | 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. |