2024/06/04 by Pratiksha Chauhan, Chauhan, Pratiksha, Samir Shukla +3 · 3 citations
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2406.01979
openalex publication_date 2024/06/04 · openalex created_date 2024/06/08 · openalex updated_date 2026/07/28
For a positive integer k, the k-cut complex of a graph G is the simplicial complex whose facets are the (|V(G)|-k)-subsets σ of the vertex set V(G) of G such that the induced subgraph of G on V(G) ∖ σ is disconnected. These complexes first appeared in the master thesis of Denker and were further studied by Bayer et al. in [Topology of cut complexes of graphs, SIAM Journal on Discrete Mathematics, 2024]. In the same article, Bayer et al. conjectured that for k ≥ 3, the k-cut complexes of squared cycle graphs are shellable. Moreover, they also conjectured about the Betti numbers of these complexes when k=3. In this article, we prove these conjectures for k=3.