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Abstract

The genus of a graph is a very basic parameter in topological graph theory, that has been the subject of extensive study. Perhaps surprisingly, despite its importance, the problem of approximating the genus of a graph is very poorly understood. It has been shown to be NPcomplete by Thomassen [Tho89], and the best known upper bound for general graphs is an O(n)-approximation that follows by Euler’s characteristic.

We give a polynomial-time pseudo-approximation algorithm for the orientable genus of Hamiltonian graphs. More specifically, on input a graph G of orientable genus g, and a Hamiltonian path in G, our algorithm computes a drawing into a surface of either orientable, or nonorientable genus g O(1).

Keywords

Hamiltonian Path Local Edge Hamiltonian Graph Elementary Band Primary Segment 
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 2013

Authors and Affiliations

  • Yury Makarychev
    • 1
  • Amir Nayyeri
    • 2
  • Anastasios Sidiropoulos
    • 3
  1. 1.Toyota Technological Institute at ChicagoUSA
  2. 2.Carnegie Mellon UniversityUSA
  3. 3.University of Illinois at Urbana–ChampaignUSA

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