Topology of Total Cut Complexes and Cut Complexes of Grid Graphs
Himanshu Chandrakar, Nisith Ranjan Hazra, Debotosh Rout, Anurag Kumar Singh · SIAM Journal on Discrete Mathematics · 2026
Abstract. Inspired by the work of Fröberg [ On Stanley-Reisner rings, in Topics in Algebra, Part 2, Banach Center Publ. 26, Part 2, PWN, Warsaw, 1990, pp. 57–70] and Eagon and Reiner [ J. Pure Appl. Algebra, 130 (1998), pp. 265–275], Bayer et al. [ SIAM J. Discrete Math., 38 (2024), pp. 1630–1675] 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 the [Formula: see text] and [Formula: see text] cases. We extend and refine the work of Bayer et al. [ SIAM J. Discrete Math., 38 (2024), pp. 1630–1675; Discrete Comput. Geom., 73 (2024), pp. 500–527; SIAM J. Discrete Math., 39 (2025), pp. 1123–1157], proving and strengthening several of their conjectures, thereby enhancing the understanding of these graph complexes’ topological and combinatorial properties.