The mathematical theory of interval graphs was developed with a view towards applications by researchers at the RAND Corporation's mathematics department, which included young researchers—such as Peter C. Fishburn and students like Alan C. Tucker and Joel E. Cohen—besides leaders—such as Delbert Fulkerson and (recurring visitor) Victor Klee.
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Applications of PQ trees include creating a contig map from DNA fragments, testing a matrix for the consecutive ones property, recognizing interval graphs and determining whether a graph is planar.