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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2018: Graph-Theoretic Concepts in Computer Science pp 252–265Cite as

On Perfect Linegraph Squares

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11159))

Abstract

A strong edge colouring is a proper colouring of the edges of a graph such that no two edges that are incident with a common edge receive the same colour. The square of a graph G is obtained from G by adding edges between vertices of distance exactly 2. Therefore the strong edge colouring problem can be transformed to the problem of finding a proper vertex colouring of the squared linegraph. In this paper we characterise families of graphs whose squared linegraphs exclude induced paths of a fixed length. As an example, we give a characterisation of graphs with \(P_4\)-free linegraph squares by a finite family of forbidden induced subgraphs. Our main result is a characterisation of graphs with perfect linegraph squares by providing forbidden induced subgraphs. In addition we are able to observe that all of these classes are \(\chi \)-bounded.

M. Hatzel and S. Wiederrecht—Both authors are supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Consolidator Grant DISTRUCT, grant agreement No 648527).

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Author information

Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Meike Hatzel & Sebastian Wiederrecht

Authors
  1. Meike Hatzel
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  2. Sebastian Wiederrecht
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Correspondence to Meike Hatzel .

Editor information

Editors and Affiliations

  1. Universität Rostock, Rostock, Germany

    Andreas Brandstädt

  2. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Ekkehard Köhler

  3. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Hatzel, M., Wiederrecht, S. (2018). On Perfect Linegraph Squares. In: Brandstädt, A., Köhler, E., Meer, K. (eds) Graph-Theoretic Concepts in Computer Science. WG 2018. Lecture Notes in Computer Science(), vol 11159. Springer, Cham. https://doi.org/10.1007/978-3-030-00256-5_21

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  • DOI: https://doi.org/10.1007/978-3-030-00256-5_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00255-8

  • Online ISBN: 978-3-030-00256-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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