# Loops in Reeb graphs of 2-manifolds

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, 2003

### Published In

- Proceedings of the Annual Symposium on Computational Geometry

### Start / End Page

- 344 - 350

### Digital Object Identifier (DOI)

- 10.1145/777842.777844

### Citation Source

- Scopus