Lower bounds on the pathwidth of some grid-like graphs ?
We present proofs of lower bounds on the node search number of some grid-like graphs including two-dimensional grids, cylinders, tori and a variation we call orb-webs. Node search number is equivalent to pathwidth and vertex separation, which are all important graph parameters. Since matching upper bounds are not difficult to obtain, this implies that the pathwidth of these graphs is easily computed, because the bounds are simple functions of the graph dimensions. We also show matching upper and lower bounds on the node search number of equidimensional tori which are one less than the obvious upper bound.
lower bounds pathwidth grids node search number cylinders tori vertex separation