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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Editor-in-Chief: Borowiecki, Mieczyslaw

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Asteroidal Quadruples in non Rooted Path Graphs

Marisa Gutierrez / Benjamin Lévêque / Silvia B. Tondato
Published Online: 2015-11-10 | DOI: https://doi.org/10.7151/dmgt.1821


A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.

Keywords: clique trees; rooted path graphs; asteroidal quadruples


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About the article

Received: 2014-05-15

Revised: 2014-12-16

Accepted: 2014-12-16

Published Online: 2015-11-10

Published in Print: 2015-11-01

Citation Information: Discussiones Mathematicae Graph Theory, Volume 35, Issue 4, Pages 603–614, ISSN (Online) 2083-5892, DOI: https://doi.org/10.7151/dmgt.1821.

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© by Marisa Gutierrez. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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