Balanced Vertex Decomposable Simplicial Complexes and their h-vectors

Balanced Vertex Decomposable Simplicial Complexes and their h-vectors

Given any finite simplicial complex ∆, we show how to construct from a colouring χ of ∆ a new simplicial complex ∆χ that is balanced and vertex decomposable. In addition, the h-vector of ∆χ is precisely the f -vector of ∆. Our construction generalizes the “whiskering” construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Coo...

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 ...

Simplicial Moves on Balanced Complexes

We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly (d + 1)-colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can ...

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.

On Isomorphism of Simplicial Complexes and Their Related Algebras