Treewidth lower bounds with brambles

Abstract

In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the characterisation of the treewidth as the maximum order of a bramble of the graph. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a lower bound for the treewidth that is at most a constant factor away from the exact treewidth. For both algorithms, we report on extensive computational experiments that show that the algorithms give often excellent lower bounds, in particular when applied to (close to) planar graphs. © Springer-Verlag Berlin Heidelberg 2005.