A Characterization of 2-Tree Proper Interval 3-Graphs
David Emory Brown, Breeann M. Flesch · Journal of Discrete Mathematics · 2014
An interval p-graph is the intersection graph of a collection of intervals which have been colored with p different colors with edges corresponding to nonempty intersection of intervals from different color classes. We characterize the class of 2-trees which are interval 3-graphs via a list of three graphs and three infinite families of forbidden induced subgraphs.