Math @ Duke

Publications [#243607] of John Harer
Papers Published
 with ColeMcLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V, Loops in Reeb graphs of 2manifolds,
Discrete and Computanional Geometry, vol. 32 no. 2
(2004),
pp. 231244
(last updated on 2018/03/20)
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 the number 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.


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