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Volume 18 Supplement 2

GraphCliques

The interval count of interval graphs and orders: a short survey

Journal of the Brazilian Computer Society volume 18, pages 103–112 (2012)Cite this article

Abstract

The interval count problem determines the smallest number of interval lengths needed in order to represent an interval model of a given interval graph or interval order. Despite the large number of studies about interval graphs and interval orders, surprisingly only a few results on the interval count problem are known. In this work, we provide a short survey about the interval count and related problems. a graph and the number of its maximal cliques.

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Author information

Affiliations

  1. COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil

    Márcia R. Cerioli, Fabiano de S. Oliveira & Jayme L. Szwarcfiter

  2. Instituto de Matemática, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal 68530, 21941-972, Rio de Janeiro, RJ, Brazil

    Márcia R. Cerioli & Jayme L. Szwarcfiter

  3. Núcleo de Computação Eletrônica, Universidade Federal do Rio de Janeiro (UFRJ), Caixa Postal: 2324, 20010-974, Rio de Janeiro, RJ, Brazil

    Jayme L. Szwarcfiter

Authors
  1. Márcia R. Cerioli
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  2. Fabiano de S. Oliveira
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  3. Jayme L. Szwarcfiter
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Corresponding author

Correspondence to Fabiano de S. Oliveira.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cerioli, M.R., de S. Oliveira, F. & Szwarcfiter, J.L. The interval count of interval graphs and orders: a short survey. J Braz Comput Soc 18, 103–112 (2012). https://doi.org/10.1007/s13173-011-0047-1

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Keywords

  • Interval count
  • Interval lengths
  • Number of lengths