On transitive orientations with restricted covering graphs

Authors:
Maria Patricia Dobson;Marisa Gutierrez;Michel Habib;Jayme L. Szwarcfiter
Affiliations:
Departamento de Matemática, Universidad Nacional de Rosario, Argentina;Departamento de Matemática, Universidad Nacional de La Plata, Argentina;Laboratoire d'Informatique Algorithmique: Fondements et Applications, Université Paris 7-Denis Diderot, Paris, France;Instituto de Matemática, NCE and COPPE, Universidade Federal do Rio de Janeiro, Brasil
Venue:
Information Processing Letters
Year:
2007

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Abstract

We consider the problem of finding a transitive orientation of a comparability graph, such that the edge set of its covering graph contains a given subset of edges. We propose a solution which employs the classical technique of modular tree decomposition. The method leads to a polynomial time algorithm to construct such an orientation or report that it does not exist.