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|Additional Physical Format:||Online version:
Dietz, Paul Frederick, 1959-
Intersection Graph Algorithms.
Ithaca, N.Y. : Cornell University, 1984
|All Authors / Contributors:||
Paul Frederick Dietz
|Description:||viii, 134 pages : illustrations ; 28 cm.|
|Series Title:||Cornell University, Department of Computer Science, TR 84-628.|
|Responsibility:||Paul F. Dietz.|
I examine another class of intersection graphs, the class of directed path graphs: intersection graphs of sets of paths in a directed tree. This class properly contains the class of interval graphs, and is properly contained by the class of chordal graphs. I give a linear time algorithm for recognizing directed path graphs and for constructing intersection representations, and a polynomial time algorithm for deciding directed path graph isomorphism.
Both algorithms use a data structure called a partial path tree, which is a kind of skeletal representation of the clique hypergraph of a directed path graph. I present linear time algorithms for finding partial path trees with specific roots and for finding partial path trees with arbitrary roots. I prove that partial path trees with identical roots are identical. Using this fact I develop a polynomial time algorithm for directed path graph isomorphism.