Proximity constraints and representable trees (extended abstract)

  • Prosenjit Bose
  • Giuseppe Di Battista
  • William Lenhart
  • Giuseppe Liotta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)

Abstract

A family of proximity drawings of graphs called open and closed β-drawings, first defined in [15], and including the Gabriel, relative neighborhood and strip drawings, are investigated. Complete characterizations of which trees admit open β-drawings for \(0 \leqslant \beta \leqslant \tfrac{1}{{2sin^2 (\pi /5)}}\)and \(\tfrac{1}{{cos(2\pi /5)}} < \beta < \infty \)or closed β-drawings for \(0 \leqslant \beta < \tfrac{1}{{2sin^2 (\pi /5)}}\)and \(\tfrac{1}{{cos(2\pi /5)}}0 \leqslant \beta \leqslant \infty \)are given, as well as partial characterizations for other values of β. For β<∞ in the intervals in which complete characterizations are given, it can be determined in linear time whether a tree admits an open or closed β-drawing, and, if so, such a drawing can be computed in linear time in the real RAM model. Finally, a complete characterization of all graphs which admit closed strip drawings is given.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Giuseppe Di Battista
    • 2
  • William Lenhart
    • 3
  • Giuseppe Liotta
    • 2
  1. 1.School of Computer ScienceMcGill University, 3480 UniversityMontréalCanada
  2. 2.Dipartimento di Informatica e SistemisticaUniversità di Roma ‘La Sapienza’RomaItalia
  3. 3.Department of Computer ScienceWilliams CollegeWilliamstown

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