Original title: Rooting algebraic vertices of convergent sequences
Authors: Hartman, David ; Hons, T. ; Nešetřil, J.
Document type: Papers
Conference/Event: EUROCOMB 2023: European Conference on Combinatorics, Graph Theory and Applications /12./, Prague (CZ), 20230828
Year: 2023
Language: eng
Abstract: Structural convergence is a framework for convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given sequence of graphs (Gn) converging to a limit L and a vertex r of L it is possible to find a sequence of vertices (rn) such that L rooted at r is the limit of the graphs Gn rooted at rn. A counterexample was found by Christofides and Král’, but they showed that the statement holds for almost all vertices r of L. We offer another perspective to the original problem by considering the size of definable sets to which the root r belongs. We prove that if r is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots (rn) always exists.
Keywords: algebraic vertices; convergent sequences; rooting
Host item entry: EUROCOMB’23. Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications
Note: Související webová stránka: https://journals.phil.muni.cz/eurocomb/article/view/35609/31523

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: https://hdl.handle.net/11104/0344128

Permalink: http://www.nusl.cz/ntk/nusl-528991


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