This article has been retracted at the authors' request; see the corrigendum at the end of the pdf file. The matching complex of a graph $G$ is a simplicial complex whose simplices are matchings in $G$. 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 $2 \times n$ grid graphs. Further in 2019, Matsushita showed that the matching complexes of $2 \times n$ grid graphs are homotopy equivalent to a wedge of spheres. In this article we prove that the matching complexes of $3\times n$ 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.
@article{10_37236_10496,
author = {Shuchita Goyal and Samir Shukla and Anurag Singh},
title = {Matching complexes of \(3 \times n\) grid graphs},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/10496},
zbl = {1482.05356},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10496/}
}
TY - JOUR
AU - Shuchita Goyal
AU - Samir Shukla
AU - Anurag Singh
TI - Matching complexes of \(3 \times n\) grid graphs
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10496/
DO - 10.37236/10496
ID - 10_37236_10496
ER -
