Treewidth Lower Bounds with Brambles [chapter]

Hans L. Bodlaender, Alexander Grigoriev, Arie M. C. A. Koster
2005 Lecture Notes in Computer Science  
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
more » ... periments that show that the algorithms give often excellent lower bounds, in particular when applied to (close to) planar graphs.
doi:10.1007/11561071_36 fatcat:hvhke4uh3nghdod5qd724jdyuq