Title: Approximating treewidth and pathwidth of some classes of perfect graphs
Abstract: In this paper we discuss algorithms that approximate the treewidth and pathwidth of cotriangulated graphs, permutation graphs and of cocomparability graphs. For a cotriangulated graph, of which the treewidth is at most k we show there exists an O(n2) algorithm finding a path-decomposition with width at most 3k+4. If G[π] is a permutation graph with treewidth k, then we show that the pathwidth of G[π] is at most 2k, and we give an algorithm which constructs a path-decomposition with width at most 2k in time O(nk). We assume that the permutation π is given. In this paper we also discuss the problem of finding an approximation for the treewidth and pathwidth of cocomparability graphs. We show that, if the treewidth of a cocomparability graph is at most k, then the pathwidth is at most O(k 2), and we give a simple algorithm finding a path-decomposition with this width. The running time of the algorithm is dominated by a coloring algorithm of the graph. Such a coloring can be found in time O(n 3). If the treewidth is bounded by some constant, previous results (i.e. [10, 21]), show that, once the approximations are given, the exact treewidth and pathwidth can be computed in linear time for all these graphs.