2006/06/15 by Massimo Caboara, Caboara, Massimo, Sara Faridi +3 · 2 citations
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Graph theory and applications #Topological and Geometric Data Analysis #math.AC #math.CO #msc:13P04
paper · pdf · doi:10.48550/arxiv.math/0606375
17 pages
arxiv created 2006/06/15 · arxiv updated 2009/12/01
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.