Matching complexes of $\bf 3 \times n$ grid graphs
Abstract
The matching complex of a graph is a simplicial complex whose simplices are matchings in . In the last few years the matching complexes of grid graphs have gained much attention among the topological combinatorists. In 2017, Braun and Hough obtained homological results related to the matching complexes of grid graphs. Further in 2019, Matsushita showed that the matching complexes of grid graphs are homotopy equivalent to a wedge of spheres. In this article we prove that the matching complexes of grid graphs are homotopy equivalent to a wedge of spheres. We also give the comprehensive list of the dimensions of spheres appearing in the wedge.
Cite
@article{arxiv.2106.09915,
title = {Matching complexes of $\bf 3 \times n$ grid graphs},
author = {Shuchita Goyal and Samir Shukla and Anurag Singh},
journal= {arXiv preprint arXiv:2106.09915},
year = {2025}
}
Comments
The proof regarding the null homotopy of inclusion maps contains an error in Sections 3.2.2, 3.2.5, 3.2.6, 3.3.1, 3.3.2, 3.3.5, 3.3.6, and 3.3.7