Loops in Reeb graphs of 2-manifolds
Cole-McLaughlin, Kree
Herbert Edelsbrunner
Harer, John
Natarajan, Vijay
Pascucci, Valerio
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.
Springer
2004
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/3985
Cole Mclaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. <i>Discrete & Computational Geometry</i>. 2004;32(2):231-244. doi:<a href="https://doi.org/10.1007/s00454-004-1122-6">10.1007/s00454-004-1122-6</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-004-1122-6
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