Geodesic
A characterization of 2-tree probe interval graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 509-527

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A graph is a probe interval graph if its vertices correspond to some set of intervals of the real line and can be partitioned into sets P and N so that vertices are adjacent if and only if their corresponding intervals intersect and at least one belongs to P. We characterize the 2-trees which are probe interval graphs and extend a list of forbidden induced subgraphs for such graphs created by Pržulj and Corneil in [2-tree probe interval graphs have a large obstruction set, Discrete Appl. Math. 150 (2005) 216-231]
Keywords: interval graph, probe interval graph, 2-tree 
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Brown, David E.; Flesch, Breeann M.; Lundgren, J. Richard. A characterization of 2-tree probe interval graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 509-527. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a3/