The geometric thickness of low degree graphs

Christian A. Duncan, David Eppstein, Stephen G. Kobourov

Research output: Contribution to conferencePaperpeer-review

43 Scopus citations

Abstract

We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. All of our algorithms run in O(n) time, where n is the number of vertices in the graph. In our proofs, we present an embedding algorithm for graphs with maximum degree three that uses an n × n grid and a more complex algorithm for embedding a graph with maximum degree four. We also show a variation using orthogonal edges for maximum degree four graphs that also uses an n × n grid. The results have implications in graph theory, graph drawing, and VLSI design.

Original languageEnglish (US)
Pages340-346
Number of pages7
StatePublished - Sep 29 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: Jun 9 2004Jun 11 2004

Other

OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
CountryUnited States
CityBrooklyn, NY
Period6/9/046/11/04

Keywords

  • Geometric thickness
  • Graph drawing
  • Graph thickness
  • Layered graphs
  • Rectangle visibility
  • Simultaneous embeddings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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