Lower bounds on the pathwidth of some grid-like graphs

Authors:
John Ellis;Robert Warren
Affiliations:
Department of Computer Science, University of Victoria, PO Box 3055, Victoria, BC, Canada V8W 3P6;School of Information Technology and Engineering, University of Ottawa, 800 King Edward Avenue, Ottawa, Ont., Canada K1N 6N5
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

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.