---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Kree
foaf_name: Cole-McLaughlin, Kree
foaf_surname: Cole Mclaughlin
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Herbert Edelsbrunner
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: John
foaf_name: Harer, John
foaf_surname: Harer
- foaf_Person:
foaf_givenName: Vijay
foaf_name: Natarajan, Vijay
foaf_surname: Natarajan
- foaf_Person:
foaf_givenName: Valerio
foaf_name: Pascucci, Valerio
foaf_surname: Pascucci
bibo_doi: 10.1007/s00454-004-1122-6
bibo_issue: '2'
bibo_volume: 32
dct_date: 2004^xs_gYear
dct_publisher: Springer@
dct_title: Loops in Reeb graphs of 2-manifolds@
...