Optimal polygonal representation of planar graphs

E. R. Gansner, Y. F. Hu, M. Kaufmann, Stephen 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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages417-432
Number of pages16
Volume6034 LNCS
DOIs
Publication statusPublished - 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)03029743
ISSN (Electronic)16113349

Other

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

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Gansner, E. R., Hu, Y. F., Kaufmann, M., & Kobourov, S. G. (2010). Optimal polygonal representation of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6034 LNCS, 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