Treewidth and Minimum Fill-in on d-Trapezoid Graphs

We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time O(n d). We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an O(n tw(G) d,1) time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid graph is part of the input. As a consequence, the minimum fill-in and the minimum interval graph completion as well as the treewidth and the pathwidth of a given trapezoid graph (or permutation graph) can be computed in time O(n²), even if no intersection model is part of the input