# Minimal Proper Interval Completions

• Ivan Rapaport
• Karol Suchan
• Ioan Todinca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)

## 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 $${{\mathcal{O}}(n+m)}$$ time algorithm computing a minimal proper interval completion of an arbitrary graph. The output is a proper interval model of the completion.

## Keywords

Maximal Clique Interval Graph Minimal Separator Arbitrary Graph Interval Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Ivan Rapaport
• 1
• Karol Suchan
• 2
• 3
• Ioan Todinca
• 2
1. 1.Departamento de Ingeniería Matemática and Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile
2. 2.LIFO, Université d’OrléansOrléansFrance
3. 3.Department of Discrete Mathematics, Faculty of Applied MathematicsAGH – University of Science and TechnologyCracowPoland