## Loops in Reeb graphs of 2-manifolds

Publication
, Journal Article

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

Published in: Discrete and Computational Geometry

January 1, 2004

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.

### Duke Scholars

## Published In

Discrete and Computational Geometry

## DOI

## ISSN

0179-5376

## Publication Date

January 1, 2004

## Volume

32

## Issue

2

## Start / End Page

231 / 244

## Related Subject Headings

- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Loops in Reeb graphs of 2-manifolds.

*Discrete and Computational Geometry*,*32*(2), 231–244. https://doi.org/10.1007/s00454-004-1122-6Cole-McLaughlin, K., H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. “Loops in Reeb graphs of 2-manifolds.”

*Discrete and Computational Geometry*32, no. 2 (January 1, 2004): 231–44. https://doi.org/10.1007/s00454-004-1122-6.Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete and Computational Geometry. 2004 Jan 1;32(2):231–44.

Cole-McLaughlin, K., et al. “Loops in Reeb graphs of 2-manifolds.”

*Discrete and Computational Geometry*, vol. 32, no. 2, Jan. 2004, pp. 231–44.*Scopus*, doi:10.1007/s00454-004-1122-6.Cole-McLaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete and Computational Geometry. 2004 Jan 1;32(2):231–244.

## Published In

Discrete and Computational Geometry

## DOI

## ISSN

0179-5376

## Publication Date

January 1, 2004

## Volume

32

## Issue

2

## Start / End Page

231 / 244

## Related Subject Headings

- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics