On the Upward Planarity of Mixed Plane Graphs

  • Fabrizio Frati
  • Michael Kaufmann
  • János Pach
  • Csaba D. Tóth
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

A mixed plane graph is a plane graph whose edge set is partitioned into a set of directed edges and a set of undirected edges. An orientation of a mixed plane graph G is an assignment of directions to the undirected edges of G resulting in a directed plane graph \(\vec G\). In this paper, we study the computational complexity of testing whether a given mixed plane graph G is upward planar, i.e., whether it admits an orientation resulting in a directed plane graph G such that G admits a planar drawing in which each edge is represented by a curve monotonically increasing in the y-direction according to its orientation.

Our contribution is threefold. First, we show that the upward planarity testing problem is solvable in cubic time for mixed outerplane graphs. Second, we show that the problem of testing the upward planarity of mixed plane graphs reduces in quadratic time to the problem of testing the upward planarity of mixed plane triangulations. Third, we exhibit linear-time testing algorithms for two classes of mixed plane triangulations, namely mixed plane 3-trees and mixed plane triangulations in which the undirected edges induce a forest.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Fabrizio Frati
    • 1
  • Michael Kaufmann
    • 2
  • János Pach
    • 3
    • 4
  • Csaba D. Tóth
    • 5
    • 6
  • David R. Wood
    • 7
  1. 1.School of Information TechnologiesThe University of SydneyAustralia
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  3. 3.EPFLLausanneSwitzerland
  4. 4.Rényi InstituteBudapestHungary
  5. 5.California State University NorthridgeUSA
  6. 6.University of CalgaryCanada
  7. 7.School of Mathematical SciencesMonash UniversityMelbourneAustralia

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