Simplicial cycles and the computation of simplicial trees

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.

• Type: Journal
• Year: 2007
• Where: JSC
• Authors: Massimo Caboara, Sara Faridi, Peter Selinger
• Keywords: JSC 2007, Simplicial, Simplicial Complex, Simplicial Complexes