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From Path Graphs to Directed Path Graphs

  • Steven Chaplick
  • Marisa Gutierrez
  • Benjamin Lévêque
  • Silvia B. Tondato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

We present a linear time algorithm to greedily orient the edges of a path graph model to obtain a directed path graph model (when possible). Moreover we extend this algorithm to find an odd sun when the method fails. This algorithm has several interesting consequences concerning the relationship between path graphs and directed path graphs. One is that for a directed path graph, path graph models and directed path graph models are the same. Another consequence concerns the difference between path graphs and directed path graphs in terms of forbidden induced subgraphs. This can be used to deduce the forbidden induced subgraph characterization of directed path graphs from the forbidden induced subgraph characterization of path graphs. The last consequence is algorithmic and shows that the recognition of directed path graphs is not more difficult than the recognition of path graphs.

Keywords

Directed Path Maximal Clique Intersection Graph Interval Graph Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Steven Chaplick
    • 1
  • Marisa Gutierrez
    • 2
  • Benjamin Lévêque
    • 3
  • Silvia B. Tondato
    • 4
  1. 1.University of TorontoCanada
  2. 2.CONICETUniversidad Nacional de La PlataArgentina
  3. 3.CNRS, LIRMMMontpellierFrance
  4. 4.Universidad Nacional de La PlataArgentina

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