In this paper we present a new technique for computing lower bounds for graph
treewidth. Our technique is based on the fact that the treewidth of a graph G is
the maximum order of a bramble of G minus one. 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 both the treewidth and branchwidth that is at most a
constant factor away from the optimum. 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
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