Topology of total cut complexes and cut complexes of grid graphs
Himanshu Chandrakar, Nisith Ranjan Hazra, Debotosh Rout, Anurag Singh

TL;DR
This paper studies the topological properties of total cut and cut complexes specifically for grid graphs, extending previous work and confirming several conjectures to deepen understanding of these complexes.
Contribution
It provides new proofs and refinements of conjectures regarding the topology of cut complexes for 2x n and 3x n grid graphs, advancing the theoretical understanding.
Findings
Proved and strengthened conjectures on the topology of cut complexes for grid graphs.
Extended the analysis of total cut complexes to specific grid graph cases.
Enhanced the theoretical framework for understanding graph complexes in combinatorics.
Abstract
Inspired by the work of Fr{\"o}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 and 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.
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Taxonomy
TopicsDigital Image Processing Techniques · Topological and Geometric Data Analysis · Computational Geometry and Mesh Generation
