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On transitive orientations of G-ê

Michael Andresen — 2009

Discussiones Mathematicae Graph Theory

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.

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