From path graphs to directed path graphs

Authors:
Steven Chaplick;Marisa Gutierrez;Benjamin Lévêque;Silvia B. Tondato
Affiliations:
University of Toronto, Canada;CONICET, Universidad Nacional de La Plata, Argentina;CNRS, LIRMM, Montpellier, France;Universidad Nacional de La Plata, Argentina
Venue:
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Year:
2010

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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.