Equilateral L-contact graphs

Steven Chaplick, Stephen G Kobourov, Torsten Ueckerdt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

Abstract

We consider L-graphs, that is contact graphs of axis-aligned L-shapes in the plane, all with the same rotation. We provide several characterizations of L-graphs, drawing connections to Schnyder realizers and canonical orders of maximally planar graphs. We show that every contact system of L's can always be converted to an equivalent one with equilateral L's. This can be used to show a stronger version of a result of Thomassen, namely, that every planar graph can be represented as a contact system of square-based cuboids. We also study a slightly more restricted version of equilateral L-contact systems and show that these are equivalent to homothetic triangle contact representations of maximally planar graphs. We believe that this new interpretation of the problem might allow for efficient algorithms to find homothetic triangle contact representations, that do not use Schramm's monster packing theorem.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages139-151
Number of pages13
Volume8165 LNCS
ISBN (Print)9783642450426
DOIs
StatePublished - 2013
Event39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013 - Lubeck, Germany
Duration: Jun 19 2013Jun 21 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8165 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013
CountryGermany
CityLubeck
Period6/19/136/21/13

Fingerprint

Equilateral
Gergonne triangle
Planar graph
Contact
Graph in graph theory
Cuboid
Graph Drawing
Packing
Efficient Algorithms
Theorem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Chaplick, S., Kobourov, S. G., & Ueckerdt, T. (2013). Equilateral L-contact graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8165 LNCS, pp. 139-151). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8165 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-45043-3_13

Equilateral L-contact graphs. / Chaplick, Steven; Kobourov, Stephen G; Ueckerdt, Torsten.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS Springer Verlag, 2013. p. 139-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8165 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chaplick, S, Kobourov, SG & Ueckerdt, T 2013, Equilateral L-contact graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8165 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8165 LNCS, Springer Verlag, pp. 139-151, 39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013, Lubeck, Germany, 6/19/13. https://doi.org/10.1007/978-3-642-45043-3_13
Chaplick S, Kobourov SG, Ueckerdt T. Equilateral L-contact graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS. Springer Verlag. 2013. p. 139-151. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45043-3_13
Chaplick, Steven ; Kobourov, Stephen G ; Ueckerdt, Torsten. / Equilateral L-contact graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8165 LNCS Springer Verlag, 2013. pp. 139-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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