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List Coloring in the Absence of Two Subgraphs

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Algorithms and Complexity (CIAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7878))

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Abstract

A list assignment of a graph G = (V,E) is a function \({\cal L}\) that assigns a list L(u) of so-called admissible colors to each u ∈ V. The List Coloring problem is that of testing whether a given graph G = (V,E) has a coloring c that respects a given list assignment \({\cal L}\), i.e., whether G has a mapping c: V → {1,2,…} such that (i) c(u) ≠ c(v) whenever uv ∈ E and (ii) c(u) ∈ L(u) for all u ∈ V. If a graph G has no induced subgraph isomorphic to some graph of a pair {H 1,H 2}, then G is called (H 1,H 2)-free. We completely characterize the complexity of List Coloring for (H 1,H 2)-free graphs.

This paper was supported by EPSRC (EP/G043434/1) and ERC (267959).

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Norway

    Petr A. Golovach

  2. School of Engineering and Computing Sciences, Durham University, UK

    Daniël Paulusma

Authors
  1. Petr A. Golovach
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  2. Daniël Paulusma
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Editors and Affiliations

  1. School of Engineering, Department of Computer Engineering and Informatics, University of Patras, 265 00, Patras, Greece

    Paul G. Spirakis

  2. LSI Department, Edif Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Maria Serna

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Golovach, P.A., Paulusma, D. (2013). List Coloring in the Absence of Two Subgraphs. In: Spirakis, P.G., Serna, M. (eds) Algorithms and Complexity. CIAC 2013. Lecture Notes in Computer Science, vol 7878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38233-8_24

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  • DOI: https://doi.org/10.1007/978-3-642-38233-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38232-1

  • Online ISBN: 978-3-642-38233-8

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