Simplicial cycles and the computation of simplicial trees

Details Simplicial cycles and the computation of simplicial trees Simplicial cycles and the computation of simplicial trees

2006-06-15

arxiv.org/abs/math/0606375v1

Mathematics

Commutative Algebra

17 pages

Scientific paper

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.

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