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Surjective H-Colouring: New Hardness Results

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem is to decide whether or not a graph G allows a homomorphism to a fixed graph H. We continue a study on a variant of this problem, namely the Surjective \(H\)-Colouring problem, which imposes the homomorphism to be vertex-surjective. We build upon previous results and show that this problem is NP-complete for every connected graph H that has exactly two vertices with a self-loop as long as these two vertices are not adjacent. As a result, we can classify the computational complexity of Surjective \(H\)-Colouring for every graph H on at most four vertices.

Supported by the Research Council of Norway via the project “CLASSIS” and the Leverhulme Trust (RPG-2016-258).

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petr A. Golovach

  2. School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, U.K.

    Matthew Johnson, Barnaby Martin, Daniël Paulusma & Anthony Stewart

Authors
  1. Petr A. Golovach
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  2. Matthew Johnson
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  3. Barnaby Martin
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  4. Daniël Paulusma
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  5. Anthony Stewart
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Corresponding author

Correspondence to Anthony Stewart .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Golovach, P.A., Johnson, M., Martin, B., Paulusma, D., Stewart, A. (2017). Surjective H-Colouring: New Hardness Results. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_26

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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