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Volume 18 Supplement 2

GraphCliques

On the classification problem for split graphs

Journal of the Brazilian Computer Society volume 18, pages 95–101 (2012)Cite this article

Abstract

The Classification Problem is the problem of deciding whether a simple graph has chromatic index equal to Δ or Δ+1. In the first case, the graphs are called Class 1, otherwise, they are Class 2. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. Split graphs are a subclass of chordal graphs. Figueiredo at al. (J. Combin. Math. Combin. Comput. 32:79–91, 2000) state that a chordal graph is Class 2 if and only if it is neighborhood-overfull. In this paper, we give a characterization of neighborhood-overfull split graphs and we show that the above conjecture is true for some split graphs.

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Author information

Affiliations

  1. Institute of Computing, University of Campinas, Campinas, Brazil

    Sheila Morais de Almeida & Célia Picinin de Mello

  2. Campus of Ponta Porã, Federal University of Mato Grosso do Sul, Ponta Porã, Brazil

    Sheila Morais de Almeida

  3. Department of Mathematics, University of Rome “La Sapienza”, Roma, Italy

    Aurora Morgana

Authors
  1. Sheila Morais de Almeida
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  2. Célia Picinin de Mello
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  3. Aurora Morgana
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Corresponding author

Correspondence to Sheila Morais de Almeida.

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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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Morais de Almeida, S., Picinin de Mello, C. & Morgana, A. On the classification problem for split graphs. J Braz Comput Soc 18, 95–101 (2012). https://doi.org/10.1007/s13173-011-0046-2

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Keywords

  • Edge-coloring
  • Overfull graph
  • Split graph
  • Classification problem