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Finding Shortest Non-separating and Non-contractible Cycles for Topologically Embedded Graphs

  • Sergio Cabello
  • Bojan Mohar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

We present an algorithm for finding shortest surface non-separating cycles in graphs with given edge-lengths that are embedded on surfaces. The time complexity is O(g 3/2 V 3/2log V + g 5/2 V 1/2), where V is the number of vertices in the graph and g is the genus of the surface. If g = o(V 1/3 − ε ), this represents a considerable improvement over previous results by Thomassen, and Erickson and Har-Peled. We also give algorithms to find a shortest non-contractible cycle in O(g \(^{O({\it g})}\) V 3/2) time, improving previous results for fixed genus.

This result can be applied for computing the (non-separating) face-width of embedded graphs. Using similar ideas we provide the first near-linear running time algorithm for computing the face-width of a graph embedded on the projective plane, and an algorithm to find the face-width of embedded toroidal graphs in O(V 5/4log V) time.

Keywords

Planar Graph Fundamental Group Homology Group Short Cycle Embed Graph 
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 2005

Authors and Affiliations

  • Sergio Cabello
    • 1
  • Bojan Mohar
    • 2
  1. 1.Department of MathematicsInstitute for Mathematics, Physics and MechanicsSlovenia
  2. 2.Department of Mathematics, Faculty of Mathematics and PhysicsUniversity of LjubljanaSlovenia

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