Jelinek2010

https://www.doi.org/10.1016/j.dam.2009.02.007

@article{Jelinek2010,
author = {Vít Jelínek},
doi = {10.1016/j.dam.2009.02.007},
issn = {0166-218X},
journaltitle = {Discrete Applied Mathematics},
number = {7},
pages = {841--850},
title = {The rank-width of the square grid},
volume = {158},
year = {2010},
}

page 2 : graph class grid has unbounded rank-width – The grid $G_{n,n}$ has rank-width equal to $n-1$.