A computationally intractable problem on simplicial complexes
Computational Geometry: Theory and Applications
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Perfect discrete Morse functions on 2-complexes
Pattern Recognition Letters
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
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This work is focused on characterizing the existence of a perfect discrete Morse function on a triangulated 3-manifold M, that is, a discrete Morse function satisfying that the numbers of critical simplices coincide with the corresponding Betti numbers. We reduce this problem to the existence of such kind of function on a spine L of M, that is, a 2-subcomplex L such that M−Δ collapses to L, where Δ is a tetrahedron of M. Also, considering the decomposition of every 3-manifold into prime factors, we prove that if every prime factor of M admits a perfect discrete Morse function, then M admits such kind of function.