Simplicial cycles and the computation of simplicial trees

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We generalize the concept of a cycle from graphs to simplicial complexes. We show that a simplicial cycle is either a sequence of facets connected in the shape of a circle, or is a cone over such a structure. We show that a simplicial tree is a connected cycle-free simplicial complex, and use this characterization to produce an algorithm that checks in polynomial time whether a simplicial complex is a tree. We also present an efficient algorithm for checking whether a simplicial complex is grafted, and therefore Cohen-Macaulay.
17 pages

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Commutative Algebra, Combinatorics, 13P04

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http://salesiana.dossiersoluciones.com/handle/123456789/113904

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606375
 http://arxiv.org/abs/math/0606375

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arXiv