  By a well known result the treewidth of k-outerplanar graphs is at most 3k-1.
This paper gives, besides a rigorous proof of this fact, an algorithmic
implementation of the proof, i.e. it is shown that, given a k-outerplanar graph
G, a tree decomposition of G of width at most 3k-1 can be found in O(kn) time
and space. Similarly, a branch decomposition of a k-outerplanar graph of width
at most 2k+1 can be also obtained in O(kn) time, the algorithm for which is
also analyzed.
