License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.38
URN: urn:nbn:de:0030-drops-160461
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Dvořák, Zdeněk ; Gonçalves, Daniel ; Lahiri, Abhiruk ; Tan, Jane ; Ueckerdt, Torsten

On Comparable Box Dimension

LIPIcs-SoCG-2022-38.pdf (0.6 MB)


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.

BibTeX - Entry

  author =	{Dvo\v{r}\'{a}k, Zden\v{e}k and Gon\c{c}alves, Daniel and Lahiri, Abhiruk and Tan, Jane and Ueckerdt, Torsten},
  title =	{{On Comparable Box Dimension}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-160461},
  doi =		{10.4230/LIPIcs.SoCG.2022.38},
  annote =	{Keywords: geometric graphs, minor-closed graph classes, treewidth fragility}

Keywords: geometric graphs, minor-closed graph classes, treewidth fragility
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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