International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 295-308 | Cite as

Recognizing and Drawing IC-Planar Graphs

  • Franz J. Brandenburg
  • Walter Didimo
  • William S. Evans
  • Philipp Kindermann
  • Giuseppe Liotta
  • Fabrizio Montecchiani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph G with n vertices, we present an O(n)-time algorithm that computes a straight-line drawing of G in quadratic area, and an \(O(n^3)\)-time algorithm that computes a straight-line drawing of G with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is \(\mathrm {NP}\)-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Franz J. Brandenburg
    • 1
  • Walter Didimo
    • 2
  • William S. Evans
    • 3
  • Philipp Kindermann
    • 4
  • Giuseppe Liotta
    • 2
  • Fabrizio Montecchiani
    • 2
  1. 1.Universität PassauPassauGermany
  2. 2.Università Degli Studi di PerugiaPerugiaItaly
  3. 3.University of British ColumbiaVancouverCanada
  4. 4.Universität WürzburgWürzburgGermany

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