A linear time algorithm for finding tree-decompositions of small treewidth

Abstract

In this paper, we give, for constant k, a linear time algorithm, that given a graph G = (V, E), determines whether the treewidth of G is at most k, and if so, finds a tree- decomposition of G with treewidth at most k. A consequence is that every minor-closed class of graphs that docs not contain all planar graphs has a linear time recognition algorithm.