Optimal polygonal representation of planar graphs

E. R. Gansner, Y. F. Hu, M. Kaufmann, S. G. Kobourov

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

7 Scopus citations

Abstract

In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear time algorithm for representing any planar graph by touching hexagons. Moreover, our algorithm produces convex polygons with edges with slopes 0, 1, -1.

Original languageEnglish (US)
Title of host publicationLATIN 2010
Subtitle of host publicationTheoretical Informatics - 9th Latin American Symposium, Proceedings
Pages417-432
Number of pages16
DOIs
StatePublished - Jun 18 2010
Event9th Latin American Theoretical Informatics Symposium, LATIN 2010 - Oaxaca, Mexico
Duration: Apr 19 2010Apr 23 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6034 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th Latin American Theoretical Informatics Symposium, LATIN 2010
CountryMexico
CityOaxaca
Period4/19/104/23/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Gansner, E. R., Hu, Y. F., Kaufmann, M., & Kobourov, S. G. (2010). Optimal polygonal representation of planar graphs. In LATIN 2010: Theoretical Informatics - 9th Latin American Symposium, Proceedings (pp. 417-432). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6034 LNCS). https://doi.org/10.1007/978-3-642-12200-2_37