Topology of total cut and cut complexes of grid graphs

Himanshu Chandrakar, Nisith Ranjan Hazra, Debotosh Rout, Anurag Singh

Published 2024-08-14Version 1

Inspired by the work of Fr\"oberg (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 the topological and combinatorial properties of these graph complexes.