

Title  Loops in Reeb graphs of 2manifolds
(Article) 
in  Discrete and Computational Geometry 
Author(s) 
Kree ColeMcLaughlin, Herbert Edelsbrunner, John Harer, Vijay Natarajan, Valerio Pascucci 
Keyword(s)  Computational topology, 2manifolds, Morse functions,
level sets, Reeb graphs, loops, algorithms. 
Year 
2004

Pages  231244 
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BibTeX  
Abstract 
Given a Morse function $f$ over a 2manifold 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 thenumber of loops in the Reeb graph that depend on the genus, the number of boundary components,and whether or not the 2manifold 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 2manifold and the Morse function.
