STACS 2007: STACS 2007 pp 236-247

# Characterizing Minimal Interval Completions

Towards Better Understanding of Profile and Pathwidth (Extended Abstract)
• Pinar Heggernes
• Karol Suchan
• Ioan Todinca
• Yngve Villanger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

## Abstract

Minimal interval completions of graphs are central in understanding two important and widely studied graph parameters: profile and pathwidth. Such understanding seems necessary to be able to attack the problem of computing these parameters. An interval completion of a given graph is an interval supergraph of it on the same vertex set, obtained by adding edges. If no subset of the added edges can be removed without destroying the interval property, we call it a minimal interval completion. In this paper, we give the first characterization of minimal interval completions. We present a polynomial time algorithm, for deciding whether a given interval completion of an arbitrary graph is minimal. If the interval completion is not minimal the algorithm can be used to extract a minimal interval completion that is a subgraph of the given interval completion.

## Keywords

Polynomial Time Algorithm Maximal Clique Interval Graph Input Graph Chordal Graph
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

• Pinar Heggernes
• 1
• Karol Suchan
• 2
• 3
• Ioan Todinca
• 2
• Yngve Villanger
• 1
1. 1.Department of Informatics, University of Bergen, N-5020 BergenNorway
2. 2.LIFO, Université d’Orleans, PB 6759, F-45067 Orleans Cedex 2France
3. 3.Faculty of Applied Mathematics, AGH - University of Science and Technology, KrakowPoland