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Computational Complexity Classification of Partition under Compaction and Retraction

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Computing and Combinatorics (COCOON 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3106))

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Abstract

The compaction and retraction problems are special graph colouring problems, and can also be viewed as partition problems with certain properties. A very close relationship between the compaction, retraction, and constraint satisfaction problems has been established earlier providing evidence that it is likely to be difficult to give a complete computational complexity classification of the compaction and retraction problems for reflexive or bipartite graphs. In this paper, we give a complete computational complexity classification of the compaction and retraction problems for all graphs (including partially reflexive graphs) with four or fewer vertices. The complexity classification of both the compaction and retraction problems is found to be the same for each of these graphs. This relates to a long-standing open problem concerning the equivalence of the compaction and retraction problems. The study of the compaction and retraction problems for graphs with at most four vertices has a special interest as it covers a popular open problem in relation to the general open problem. We also give complexity results for some general graphs.

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Author information

Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6

    Narayan Vikas

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  1. Narayan Vikas
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Editor information

Editors and Affiliations

  1. Division of Computer Science, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

    Kyung-Yong Chwa

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    J. Ian J. Munro

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© 2004 Springer-Verlag Berlin Heidelberg

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Vikas, N. (2004). Computational Complexity Classification of Partition under Compaction and Retraction. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_41

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  • DOI: https://doi.org/10.1007/978-3-540-27798-9_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22856-1

  • Online ISBN: 978-3-540-27798-9

  • eBook Packages: Springer Book Archive

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