2022/09/06 by Margaret M. Bayer, Margaret Bayer, Bayer, Margaret +4
Computer Science · Mathematics · #05C70 #05E45 #55P15 #57M15 #Advanced Combinatorial Mathematics #Combinatorics #Combinatorics (math.CO) #Contractible space #Discrete mathematics #FOS: Mathematics #Geometry #Graph #Homotopy #Homotopy and Cohomology in Algebraic Topology #Honeycomb #Matching (statistics) #Mathematical proof #Mathematics #Physics #Pure mathematics #SPHERES #Simplicial complex #Topological and Geometric Data Analysis #Wedge (geometry) #math.CO #msc:05C70 #msc:05E45 #msc:55P15 #msc:57M15
paper · pdf · doi:10.48550/arxiv.2209.02803
published in arXiv (Cornell University) (Cornell University) · 28 pages
arxiv created 2022/09/06 · openalex publication_date 2022/09/06 · arxiv updated 2022/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.