ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 29(3) (2009) 423-467


Michael Andresen

Fakultät für Mathematik
PSF 4120, 39016 Magdeburg, Germany


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: (primary): comparability graph, edge deletion;
(secondary): transitive orientation, Triangle Lemma, Γ-components, open shop scheduling, irreducibility.

2000 Mathematics Subject Classification: 05C75, 05C20, 90B35, 68R10.


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Received 28 February 2007
Revised 18 February 2009
Accepted 18 February 2009