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Δ-List Vertex Coloring in Linear Time

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Algorithm Theory — SWAT 2002 (SWAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2368))

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Abstract

We present a new proof of a theorem of Erdős, Rubin, and Taylor, which states that the list chromatic number (or choice number) of a connected, simple graph that is neither complete nor an odd cycle does not exceed its maximum degree Δ. Our proof yields the first-known linear-time algorithm to Δ-list-color graphs satisfying the hypothesis of the theorem. Without change, our algorithm can also be used to Δ-color such graphs. It has the same running time as, but seems to be much simpler than, the current known algorithm, due to Lovász, for Δ-coloring such graphs. We also give a specialized version of our algorithm that works on subcubic graphs (ones with maximum degree three) by exploiting a simple decomposition principle for them.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 80309, USA

    San Skulrattanakulchai

Authors
  1. San Skulrattanakulchai
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Kuopio, P.O. Box 1627, 70211, Kuopio, Finland

    Martti Penttonen

  2. BRICS, University of Aarhus, Department of Computer Science, NY Munkegade, 8000, Aarhus C, Denmark

    Erik Meineche Schmidt

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© 2002 Springer-Verlag Berlin Heidelberg

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Skulrattanakulchai, S. (2002). Δ-List Vertex Coloring in Linear Time. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_25

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  • DOI: https://doi.org/10.1007/3-540-45471-3_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43866-3

  • Online ISBN: 978-3-540-45471-7

  • eBook Packages: Springer Book Archive

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