From Path Graphs to Directed Path Graphs

Steven Chaplick; Marisa Gutierrez; Benjamin Lévêque; Silvia B. Tondato

doi:10.1007/978-3-642-16926-7_24

From Path Graphs to Directed Path Graphs

Steven Chaplick, Marisa Gutierrez, Benjamin Lévêque, Silvia B. Tondato

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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.keywordsdirected pathmaximal cliqueintersection graphinterval graphchordal graphthese 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.

Original language	English
Title of host publication	Graph Theoretic Concepts in Computer Science. WG 2010
Editors	D.M. Thilikos
Pages	256-265
DOIs	https://doi.org/10.1007/978-3-642-16926-7_24
Publication status	Published - 2010
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	6410
ISSN	0302-9743

Access to Document

10.1007/978-3-642-16926-7_24

Cite this

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title = "From Path Graphs to Directed Path Graphs",

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.keywordsdirected pathmaximal cliqueintersection graphinterval graphchordal graphthese 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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language = "English",

series = "Lecture Notes in Computer Science",

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From Path Graphs to Directed Path Graphs. / Chaplick, Steven; Gutierrez, Marisa; Lévêque, Benjamin et al.
Graph Theoretic Concepts in Computer Science. WG 2010. ed. / D.M. Thilikos. 2010. p. 256-265 (Lecture Notes in Computer Science, Vol. 6410).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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PY - 2010

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