Reference to lower bound on separator in a grid?
Looks like the book "Graph separators, with applications" by Arnold Rosenberg and Lenwood Heath answers your question (see section 4.3.4.), but it could happen that I misunderstood their notation (please, let me know). Anyway, this book is a very comprehensive reference on separators.

EDIT. Here is a download link on Springer: http://www.springerlink.com/content/978-0-306-46464-5