On Comparable Box Dimension

Authors Zdeněk Dvořák, Daniel Gonçalves, Abhiruk Lahiri, Jane Tan, Torsten Ueckerdt

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Zdeněk Dvořák
  • Charles University, Prague, Czech Republic
Daniel Gonçalves
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Abhiruk Lahiri
  • Charles University, Prague, Czech Republic
Jane Tan
  • Mathematical Institute, University of Oxford, UK
Torsten Ueckerdt
  • Karlsruhe Institute of Technology, Germany


This research was carried out at the workshop on Geometric Graphs and Hypergraphs organized by Yelena Yuditsky and Torsten Ueckerdt in September 2021. We would like to thank the organizers and all participants for creating a friendly and productive environment.

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Zdeněk Dvořák, Daniel Gonçalves, Abhiruk Lahiri, Jane Tan, and Torsten Ueckerdt. On Comparable Box Dimension. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Two boxes in ℝ^d are comparable if one of them is a subset of a translation of the other one. The comparable box dimension of a graph G is the minimum integer d such that G can be represented as a touching graph of comparable axis-aligned boxes in ℝ^d. We show that proper minor-closed classes have bounded comparable box dimension and explore further properties of this notion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graphs and surfaces
  • geometric graphs
  • minor-closed graph classes
  • treewidth fragility


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