In this paper we present a new technique for computing lower bounds for graph\ud treewidth. Our technique is based on the fact that the treewidth of a graph G is\ud the maximum order of a bramble of G minus one. We give two algorithms: one\ud for general graphs, and one for planar graphs. The algorithm for planar graphs is\ud shown to give a lower bound for both the treewidth and branchwidth that is at most a\ud constant factor away from the optimum. For both algorithms, we report on extensive\ud computational experiments that show that the algorithms give often excellent lower\ud bounds, in particular when applied to (close to) planar graphs
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