Interval Graph
A Graph 
is an interval graph if it captures the IntersectionRelation for some set of Intervals on the Real Line. Formally, 
is an interval graphprovided that one can assign to each 
an interval 
such that 
is nonempty precisely when 
.
References
Booth, K. S. and Lueker, G. S. ``Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity using PQ-Tree Algorithms.'' J. Comput. System Sci. 13, 335-379, 1976. Fishburn, P. C. Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. New York: Wiley, 1985. Gilmore, P. C. and Hoffman, A. J. ``A Characterization of Comparability Graphs and of Interval Graphs.'' Canad. J. Math. 16, 539-548, 1964. Lekkerkerker, C. G. and Boland, J. C. ``Representation of a Finite Graph by a Set of Intervals on the Real Line.'' Fund. Math. 51, 45-64, 1962.
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