Independence complexes of $(n\times 4)$ and $(n\times 5)$-grid graphs

Abstract

We determine the homotopy types of the independence complexes of $(n\times 4)$ and $(n\times 5)$-square grid graphs. In fact, they are homotopy equivalent to wedges of spheres.

20 pages, 15 figures, minor revision, to appear in Topology and its Applications