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First order limits of sparse graphs: Plane trees and path‐width
Author(s) -
Gajarský Jakub,
Hliněný Petr,
Kaiser Tomáš,
Král’ Daniel,
Kupec Martin,
Obdržálek Jan,
Ordyniak Sebastian,
Tůma Vojtěch
Publication year - 2017
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20676
Subject(s) - limit of a sequence , limit (mathematics) , sequence (biology) , mathematics , path (computing) , bounded function , combinatorics , tree (set theory) , longest path problem , plane (geometry) , convergence (economics) , order (exchange) , limit point , discrete mathematics , chordal graph , graph , computer science , mathematical analysis , geometry , genetics , finance , economics , biology , programming language , economic growth
Abstract 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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 612–635, 2017