Pseudo-Interval Graphs

We study a class of perfect graphs which, because they generalize interval graphs, we call pseudo-interval graphs. Like interval graphs, their vertices correspond to intervals of a linearly ordered set, but a modified definition of intersection is used in order to determine edges. The complements of pseudo-interval graphs are comparability graphs but unlike interval graphs, pseudo-interval graphs are only weakly triangulated. We characterize trees and complements of trees which are pseudo-interval graphs. Finally we determine all minimal non-pseudointerval graphs on eight or fewer vertices whose complements are comparability graphs and which are weakly triangulated. © 1995 John Wiley & Sons; Inc.