2022/11/28 by Dancheng Lu, Zexin Wang, Lu, Dancheng +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2211.15796
For a simple graph G, assume that J(G) is the vertex cover ideal of G and J(G)(s) is the s-th symbolic power of J(G). We prove that (J(C)(s))=(J(C)s) for all s≥ 1 and for all odd cycle C. For a simplicial complex Δ, we show that Δ is vertex decomposable if IΔ\vee is weakly polymatroidal. Let W=Gπ be a fully clique-whiskering graph, we prove that J(W)s is weakly polymatroidal for all s≥ 1.