Triangulating multitolerance graphs

In this paper we introduce a new class of graphs which generalize both the tolerance and the trapezoid graphs, the multitolerance graphs. We show that the difference between the pathwidth and the treewidth of a multitolerance graph is at most one, and we develop an algorithm which solves the minimum fill-in problem for a multitolerance graph with a given representation in polynomial time. These results complement the recent results of Habib and Mohring [18, 25] about the treewidth and pathwidth of cocomparability graphs and graphs without asteroidal triples, and those of Kloks et al, [21] about the minimum fill-in problem. (C) 1998 Elsevier Science B.V. All rights reserved.