2019/05/25 by Marija Jelić Milutinović, Milutinović, Marija Jelić, Helen Jenne +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Binary tree #Combinatorics #Combinatorics (math.CO) #Complex Network Analysis Techniques #Contractible space #Discrete Morse theory #Discrete mathematics #FOS: Mathematics #Homotopy #Markov Chains and Monte Carlo Methods #Matching (statistics) #Mathematics #Morse theory #Pure mathematics #Simplicial complex #Topological and Geometric Data Analysis #Tree (set theory) #Wedge (geometry) #math.AT #math.CO
paper · pdf · doi:10.48550/arxiv.1905.10560
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/05/25 · arxiv created 2021/01/28 · arxiv updated 2021/02/01 · openalex created_date 2022/10/05 · openalex updated_date 2026/08/05
A matching complex of a simple graph G is a simplicial complex with faces given by the matchings of G. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that matching complexes of forests are contractible or homotopy equivalent to a wedge of spheres. We study two specific families of trees. For caterpillar graphs, we give explicit formulas for the number of spheres in each dimension and for perfect binary trees we find a strict connectivity bound. We also use a tool from discrete Morse theory called the Matching Tree Algorithm to study the connectivity of honeycomb graphs, partially answering a question raised by Jonsson.