Planar Drawings of Higher-Genus Graphs

  • Christian A. Duncan
  • Michael T. Goodrich
  • Stephen G. Kobourov
Conference paper

DOI: 10.1007/978-3-642-11805-0_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)
Cite this paper as:
Duncan C.A., Goodrich M.T., Kobourov S.G. (2010) Planar Drawings of Higher-Genus Graphs. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg

Abstract

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface \(\cal S\) of genus g and produce a planar drawing of G in R2, with a bounding face defined by a polygonal schema \(\cal P\) for \(\cal S\). Our drawings are planar, but they allow for multiple copies of vertices and edges on \(\cal P\)’s boundary, which is a common way of visualizing higher-genus graphs in the plane. As a side note, we show that it is NP-complete to determine whether a given graph embedded in a genus-g surface has a set of 2g fundamental cycles with vertex-disjoint interiors, which would be desirable from a graph-drawing perspective.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christian A. Duncan
    • 1
  • Michael T. Goodrich
    • 2
  • Stephen G. Kobourov
    • 3
  1. 1.Dept. of Computer ScienceLouisiana Tech Univ 
  2. 2.Dept. of Computer ScienceUniv. of CaliforniaIrvine
  3. 3.Dept. of Computer ScienceUniversity of Arizona 

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