2004/10/15 by Svante Linusson, Linusson, Svante, John Shareshian +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.math/0410345
20 pages
arxiv created 2004/10/15 · openalex publication_date 2004/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For positive integers k,n, we investigate the simplicial complex NMk(n) of all graphs G on vertex set [n] such that every matching in G has size less than k. This complex (along with other associated cell complexes) is found to be homotopy equivalent to a wedge of spheres. The number and dimension of the spheres in the wedge are determined, and (partially conjectural) links to other combinatorially defined complexes are described. In addition we study for positive integers r,s and k the simplicial complex BNMk(n) of all bipartite graphs G on bipartition [r] ∪ [s] such that there is no matching of size k in G, and obtain results similar to those obtained for NMk(n).