Loops in Reeb graphs of 2-manifolds

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V

Published Date

  • January 1, 2004

Published In

Volume / Issue

  • 32 / 2

Start / End Page

  • 231 - 244

International Standard Serial Number (ISSN)

  • 0179-5376

Digital Object Identifier (DOI)

  • 10.1007/s00454-004-1122-6

Citation Source

  • Scopus