Simplicial cycles and the computation of simplicial trees
Commutative Algebra
2007-05-23 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0606375,
title = {Simplicial cycles and the computation of simplicial trees},
author = {Massimo Caboara and Sara Faridi and Peter Selinger},
journal= {arXiv preprint arXiv:math/0606375},
year = {2007}
}
Comments
17 pages