2022/09/06 by Margaret M. Bayer, Bayer, Margaret, Marija Jelić Milutinović +3
Computer Science · Mathematics · #05C70 #05E45 #55P15 #57M15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2209.02803
openalex publication_date 2022/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The \em perfect matching complex of a graph is the simplicial complex on the edge set of the graph with facets corresponding to perfect matchings of the graph. This paper studies the perfect matching complexes, Mp(Hk × m× n), of honeycomb graphs. For k = 1, Mp(H1× m× n) is contractible unless n≥ m=2, in which case it is homotopy equivalent to the (n-1)-sphere. Also, Mp(H2× 2× 2) is homotopy equivalent to the wedge of two 3-spheres. The proofs use discrete Morse theory.