Minimal proper interval completions

Authors:
Ivan Rapaport;Karol Suchan;Ioan Todinca
Affiliations:
Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile;Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile and Department of Discrete Mathematics, Faculty of Applied Mathema ...;LIFO, Université d'Orléans, 45067 Orléans Cedex 2, France and LRI, Université Paris XI, France
Venue:
Information Processing Letters
Year:
2008

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Abstract

Given an arbitrary graph G=(V,E) and a proper interval graph H=(V,F) with E@?F we say that H is a proper interval completion of G. The graph H is called a minimal proper interval completion of G if, for any sandwich graph H^'=(V,F^') with E@?F^'@?F, H^' is not a proper interval graph. In this paper we give a O(n+m) time algorithm computing a minimal proper interval completion of an arbitrary graph. The output is a proper interval model of the completion.