Linear colorings of simplicial complexes and collapsing

Solving 1-Laplacians in Nearly Linear Time: Collapsing and Expanding a Topological Ball

Abstract We present an e cient algorithm for solving a linear system arising from the 1-Laplacian of a collapsible simplicial complex with a known collapsing sequence. When combined with a result of Chillingworth, our algorithm is applicable to convex simplicial complexes embedded in R. The running time of our algorithm is nearly-linear in the size of the complex and is logarithmic on its numer...

On Isomorphism of Simplicial Complexes and Their Related Algebras

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 ...

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

Chromatic Polynomials of Simplicial Complexes

In this note we consider s-chromatic polynomials for finite simplicial complexes. When s = 1, the 1-chromatic polynomial is just the usual graph chromatic polynomial of the 1-skeleton. In general, the s-chromatic polynomial depends on the s-skeleton and its value at r is the number of (r, s)-colorings of the simplicial complex.