A characterization of uniquely representable interval graphs

Abstract An alternative to Hanlon's buried-subgraph characterization of interval graphs that have unique (up to duality) agreeing interval orders is proveded. The alternative is based on a relation L between ordered pairs of points that are adjacent in the interval graph. The interpretation of abLxy is that if the interval for a precedes (follows) the interval for b in a representation of the interval graph, then the interval for x must precede (follow) the interval for y.