Discrete & Computational Geometry

, Volume 32, Issue 2, pp 231–244 | Cite as

Loops in Reeb Graphs of 2-Manifolds

  • Kree Cole-McLaughlinEmail author
  • Herbert EdelsbrunnerEmail author
  • John HarerEmail author
  • Vijay NatarajanEmail author
  • Valerio PascucciEmail author


Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.


Lower Bound Boundary Component Morse Function Reeb Graph 
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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551USA
  2. 2.Department of Mathematics, Duke University, Durham, NC 27708USA
  3. 3.Department of Computer Science, Duke University, Durham, NC 27708USA
  4. 4.Raindrop Geomagic, Research Triangle Park, NC 27709USA

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