Independence complexes of $(n \times 6)$-grid graphs

TL;DR

This paper determines the homotopy types of independence complexes for (n x 6)-grid graphs, showing they are homotopy equivalent to wedges of spheres, thus advancing understanding of their topological structure.

Contribution

It provides the first complete characterization of the homotopy types of independence complexes for (n x 6)-grid graphs, revealing they are wedges of spheres.

Findings

Independence complexes are homotopy equivalent to wedges of spheres.

Homotopy types are explicitly determined for (n x 6)-grid graphs.

Results contribute to topological combinatorics and graph theory.

Abstract

We determine the homotopy types of the independence complexes of the $(n \times 6)$-square grid graphs. In fact, we show that these complexes are homotopy equivalent to wedges of spheres.