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Planar Drawings of Higher-Genus Graphs

  • Christian A. Duncan
  • Michael T. Goodrich
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)

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 R 2, 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.

Keywords

Outer Face External Face Fundamental Cycle Topological Disk Planar Drawing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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