Optimal polygonal representation of planar graphs

C. A. Duncan, E. R. Gansner, Y. F. Hu, M. Kaufmann, Stephen G Kobourov

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

In this paper, we consider the problem of representing planar 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 having at most three slopes and with all vertices lying on an O(n) ×O(n) grid.

Original languageEnglish (US)
Pages (from-to)672-691
Number of pages20
JournalAlgorithmica
Volume63
Issue number3
DOIs
StatePublished - 2012

Keywords

  • Contact graphs
  • Graph drawing
  • Planar graphs
  • Polygonal drawings

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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