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Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

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Computer Science – Theory and Applications (CSR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6651))

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Abstract

A homomorphism from a graph G to a graph H is a vertex mapping f:V G  → V H such that f(u) and f(v) form an edge in H whenever u and v form an edge in G. The H-Coloring problem is to test whether a graph G allows a homomorphism to a given graph H. A well-known result of Hell and Nešetřil determines the computational complexity of this problem for any fixed graph H. We study a natural variant of this problem, namely the Surjective H -Coloring problem, which is to test whether a graph G allows a homomorphism to a graph H that is (vertex-)surjective. We classify the computational complexity of this problem when H is any fixed partially reflexive tree. Thus we identify the first class of target graphs H for which the computational complexity of Surjective H -Coloring can be determined. For the polynomial-time solvable cases, we show a number of parameterized complexity results, especially on nowhere dense graph classes.

This work has been supported by EPSRC (EP/G043434/1).

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Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, UK

    Petr A. Golovach, Daniël Paulusma & Jian Song

Authors
  1. Petr A. Golovach
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  2. Daniël Paulusma
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  3. Jian Song
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Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia

    Alexander Kulikov

  2. Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia

    Nikolay Vereshchagin

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Golovach, P.A., Paulusma, D., Song, J. (2011). Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_20

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  • DOI: https://doi.org/10.1007/978-3-642-20712-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20711-2

  • Online ISBN: 978-3-642-20712-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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