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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 n and 3 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.
Chandrakar et al. (Wed,) studied this question.