We present proofs of lower bounds on the node search number of some grid-like graphs including 2-dimensional grids, cylinders, tori and some variations thereof. 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 on the Pathwidth of some Grid-like Graphs (PDF)

J. Ellis and R. Warren

to appear in Discrete Applied Math.