Constructive linear time algorithms for branchwidth

Abstract

Let Qk be the class of graphs with branchwidth at most k. In this paper we prove that one can construct, for any k, a linear time algorithm that checks if a graph belongs to Gk and, if so, outputs a branch decomposition of minimum width. Moreover, we find the obstruction set for G3, and, for the same class, we give a safe and complete set of reduction rules. Our results lead to a practical linear time algorithm that checks if a graph has branchwidth ≤ 3 and, if so, outputs a branch decomposition of minimum width.