First order limits of sparse graphs: Plane trees and path-width
Combinatorics
2016-04-01 v3
Abstract
Nesetril 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.
Keywords
Cite
@article{arxiv.1504.08122,
title = {First order limits of sparse graphs: Plane trees and path-width},
author = {Jakub Gajarsky and Petr Hlineny and Tomas Kaiser and Daniel Kral and Martin Kupec and Jan Obdrzalek and Sebastian Ordyniak and Vojtech Tuma},
journal= {arXiv preprint arXiv:1504.08122},
year = {2016}
}