Cole-McLaughlin, Kree; Edelsbrunner, HerbertIST Austria ; 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.
Discrete & Computational Geometry
Partially supported by NSF under Grants EIA-99-72879 and CCR-00-86013.
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Cole Mclaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry. 2004;32(2):231-244. doi:10.1007/s00454-004-1122-6
Cole Mclaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry, 32(2), 231–244. https://doi.org/10.1007/s00454-004-1122-6
Cole Mclaughlin, Kree, Herbert Edelsbrunner, John Harer, Vijay Natarajan, and Valerio Pascucci. “Loops in Reeb Graphs of 2-Manifolds.” Discrete & Computational Geometry 32, no. 2 (2004): 231–44. https://doi.org/10.1007/s00454-004-1122-6.
K. Cole Mclaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, “Loops in Reeb graphs of 2-manifolds,” Discrete & Computational Geometry, vol. 32, no. 2, pp. 231–244, 2004.
Cole Mclaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. 2004. Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry. 32(2), 231–244.
Cole Mclaughlin, Kree, et al. “Loops in Reeb Graphs of 2-Manifolds.” Discrete & Computational Geometry, vol. 32, no. 2, Springer, 2004, pp. 231–44, doi:10.1007/s00454-004-1122-6.