Algebraic shifting of strongly edge decomposable spheres

Algebraic shifting and strongly edge decomposable complexes

Let Γ be a simplicial complex with n vertices, and let ∆(Γ) be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If Γ is a simplicial sphere, then it is known that (a) ∆(Γ) is pure and (b) h-vector of Γ is symmetric. Kalai and Sarkaria conjectured that if Γ is a simplicial sphere then its algebraic shifting also satisfies (c) ∆(Γ) ⊂ ∆(C(n, d)), where C(n,...

Spheres arising from multicomplexes

In 1992, Thomas Bier introduced a surprisingly simply way to construct a large number of simplicial spheres. He proved that, for any simplicial complex ∆ on the vertex set V with ∆ 6= 2 , the deleted join of ∆ with its Alexander dual ∆∨ is a combinatorial sphere. In this paper, we extend Bier’s construction to multicomplexes, and study their combinatorial and algebraic properties. We show that ...

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

Constructing vertex decomposable graphs

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.