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 does not contain all planar graphs
has a linear time recognition algorithm. Another consequence is that a similar
result holds when we look instead for path-decompositions with pathwidth at
most some constant k.