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Upward Planar Morphs

  • Giordano Da LozzoEmail author
  • Giuseppe Di Battista
  • Fabrizio Frati
  • Maurizio Patrignani
  • Vincenzo Roselli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

We prove that, given two topologically-equivalent upward planar straight-line drawings of an n-vertex directed graph G, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O(1) morphing steps if G is a reduced planar st-graph, O(n) morphing steps if G is a planar st-graph, O(n) morphing steps if G is a reduced upward planar graph, and \(O(n^2)\) morphing steps if G is a general upward planar graph. Further, we show that \(\varOmega (n)\) morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an n-vertex path.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Giordano Da Lozzo
    • 1
    Email author
  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
  • Maurizio Patrignani
    • 1
  • Vincenzo Roselli
    • 1
  1. 1.Roma Tre UniversityRomeItaly

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