TY - JOUR
AB - 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.
AU - Cole-McLaughlin, Kree
AU - Herbert Edelsbrunner
AU - Harer, John
AU - Natarajan, Vijay
AU - Pascucci, Valerio
ID - 3985
IS - 2
JF - Discrete & Computational Geometry
TI - Loops in Reeb graphs of 2-manifolds
VL - 32
ER -