“…On the other hand, for some special classes of graphs, e.g., permutation graphs, cotriangulated graphs, convex graphs, chordal bipartite graphs, and circle graphs, there exist polynomial time algorithms to determine the treewidth (see, e.g., [24]). For graphs with constant treewidth an algorithm for constructing a minimal tree-decomposition is described in [6]. This algorithm works in time O log 2 n using O n operations on a EREW PRAM.…”