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Combinatorica

, Volume 38, Issue 5, pp 1129–1148 | Cite as

Sparsity and Dimension

  • Gwenaël Joret
  • Piotr Micek
  • Veit Wiechert
Original Paper
  • 21 Downloads

Abstract

We prove that posets of bounded height whose cover graphs belong to a fixed class with bounded expansion have bounded dimension. Bounded expansion, introduced by Nešetřil and Ossona de Mendez as a model for sparsity in graphs, is a property that is naturally satisfied by a wide range of graph classes, from graph structure theory (graphs excluding a minor or a topological minor) to graph drawing (e.g. graphs with bounded book thickness). Therefore, our theorem generalizes a number of results including the most recent one for posets of bounded height with cover graphs excluding a fixed graph as a topological minor. We also show that the result is in a sense best possible, as it does not extend to nowhere dense classes; in fact, it already fails for cover graphs with locally bounded treewidth.

Mathematics Subject Classification (2000)

06A07 05C35 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Theoretical Computer Science Department Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  3. 3.Institut für MathematikTechnische Universität BerlinBerlinGermany

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