Geodesic
On transitive orientations of G-ê
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 423-467.

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A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.
Keywords: comparability graph, edge deletion, transitive orientation, Triangle Lemma, Γ-components, open shop scheduling, irreducibility 
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Andresen, Michael. On transitive orientations of G-ê. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 423-467. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a0/

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