Title:	First order limits of sparse graphs: Plane trees and path-width
Authors:	Gajarský, Jakub Hliněný, Petr Kaiser, Tomáš Král', Daniel Kupec, Martin Obdržálek, Jan Ordyniak, Sebastian Tůma, Vojtěch
Citation:	GAJARSKÝ, J., HLINĚNÝ, P., KAISER, T., KRÁL', D., KUPEC, M., OBDRŽÁLEK, J., ORDYNIAK, S., TŮMA, V. First order limits of sparse graphs: Plane trees and path-width. Random structures & algorithms, 2017, roč. 50, č. 4, s. 612-635. ISSN 1042-9832.
Issue Date:	2017
Publisher:	Wiley
Document type:	preprint preprint
URI:	http://hdl.handle.net/11025/29280
ISSN:	1042-9832
Keywords:	grafový limit;konvergence prvního řádu;modelování;cesta-šířka
Keywords in different language:	graph limit;first order convergence;modeling;path-width
Abstract in different language:	Nešetřil and Ossona de Mendez introduced the notion of first order convergence as an attempt to unify the notions of convergence for sparse and dense graphs. It is known that there exist first order convergent sequences of graphs with no limit modeling (an analytic representation of the limit). On the positive side, every first order convergent sequence of trees or graphs with no long path (graphs with bounded tree-depth) has a limit modeling. We strengthen these results by showing that every first order convergent sequence of plane trees (trees with embeddings in the plane) and every first order convergent sequence of graphs with bounded path-width has a limit modeling.
Rights:	Plný text je přístupný v rámci univerzity přihlášeným uživatelům. © Wiley
Appears in Collections:	Články / Articles (KMA) Preprinty / Preprints (KMA) OBD

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