Topology of total cut complexes and cut complexes of grid graphs

Abstract

Inspired by the work of Fr{ö}berg (1990) and Eagon and Reiner (1998), Bayer et al. recently introduced two new graph complexes: total cut complexes and cut complexes. In this article, we investigate these complexes specifically for (rectangular) grid graphs, focusing on $2\times n$ and $3\times n$ cases. We extend and refine the work of Bayer et al., proving and strengthening several of their conjectures, thereby enhancing the understanding of these graph complexes' topological and combinatorial properties.

To appear in the SIAM Journal on Discrete Mathematics