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;LIFO, Université d'Orléans, Orléans, France;LIFO, Université d'Orléans, Orléans, France
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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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 time algorithm computing a minimal proper interval completion of an arbitrary graph. The output is a proper interval model of the completion.