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Coloring Algorithms on Subcubic Graphs

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

We present efficient algorithms for three coloring problems on subcubic graphs (ones with maximum degree 3). These algorithms are based on a simple decomposition principle for subcubic graphs. The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. As evidence we give the first randomized EREW PRAM algorithm that uses O(n/log n) processors and runs in O(log n) time with high probability, where n is the number of vertices of the input graph. The second algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The third algorithm generalizes this to the first linear-time algorithm to 5-list-total-color subcubic graphs.

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Author information

Authors and Affiliations

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

    Harold N. Gabow & San Skulrattanakulchai

Authors
  1. Harold N. Gabow
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  2. San Skulrattanakulchai
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Gabow, H.N., Skulrattanakulchai, S. (2002). Coloring Algorithms on Subcubic Graphs. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_9

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  • DOI: https://doi.org/10.1007/3-540-45655-4_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

  • eBook Packages: Springer Book Archive

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