Strictly Interval Graphs: Characterization and Linear Time Recognition

In this paper we introduce a new subclass of chordal graphs, those which are simultaneously strictly chordal and interval, the strictly interval graphs. We present the characterization of the new class by forbidden subgraphs and a simple linear time recognition obtained directly from the determination of the leafage of strictly chordal graphs. We also show how strictly interval graphs relate to proper interval graphs, presenting the new hierarchy of classes.