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## Details

Additional Physical Format: | Online version: Dietz, Paul Frederick, 1959- Intersection Graph Algorithms. Ithaca, N.Y. : Cornell University, 1984 (OCoLC)704420872 |
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Material Type: | Thesis/dissertation |

Document Type: | Book |

All Authors / Contributors: |
Paul Frederick Dietz |

OCLC Number: | 13399697 |

Description: | viii, 134 pages : illustrations ; 28 cm. |

Series Title: | Cornell University, Department of Computer Science, TR 84-628. |

Responsibility: | Paul F. Dietz. |

### Abstract:

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.

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