Homology, Homotopy and Applications

Volume 26 (2024)

Number 1

Independence complexes of $(n \times 6)$-grid graphs

Pages: 15 – 27

DOI: https://dx.doi.org/10.4310/HHA.2024.v26.n1.a2


Takahiro Matsushita (Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto, Nagano, Japan)

Shun Wakatsuki (Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Japan)


We determine the homotopy types of the independence complexes of the $(n \times 6)$-square grid graphs. In fact, we show that these complexes are homotopy equivalent to wedges of spheres.


independence complex, square grid graph

2010 Mathematics Subject Classification

05C69, 55P10

Received 31 July 2022

Received revised 27 January 2023

Accepted 27 January 2023

Published 24 January 2024