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 whic
h 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 trip
les, and those of Kloks et al, [21] about the minimum fill-in problem.
(C) 1998 Elsevier Science B.V. All rights reserved.