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Simplicial cycles and the computation of simplicial trees

Massimo Caboara·Sara Faridi·Peter Selinger
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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.

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Massimo Caboara, Sara Faridi, Peter Selinger. 2006-06-15. Simplicial cycles and the computation of simplicial trees. https://arxiv.org/abs/math/0606375

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