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The Complexity of the Partition Coloring Problem

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Theory and Applications of Models of Computation (TAMC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12337))

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Abstract

Given a simple undirected graph \(G=(V,E)\) and a partition of the vertex set V into p parts, the Partition Coloring Problem asks if we can select one vertex from each part of the partition such that the chromatic number of the subgraph induced on the p selected vertices is bounded by k. PCP is a generalized problem of the classical Vertex Coloring Problem and has applications in many areas, such as scheduling and encoding, etc. In this paper, we show the complexity status of the Partition Coloring Problem with three parameters: the number of colors, the number of parts of the partition, and the maximum size of each part of the partition. Furthermore, we give a new exact algorithm for this problem.

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Notes

  1. 1.

    The notation \(O^*\) is a modified big-O notation that suppresses all polynomially bounded factors.

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Zhenyu Guo, Mingyu Xiao & Yi Zhou

Authors
  1. Zhenyu Guo
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  2. Mingyu Xiao
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  3. Yi Zhou
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Corresponding author

Correspondence to Zhenyu Guo .

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Editors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, USA

    Jianer Chen

  2. School of Computer Science and Engineering, Central South University, Changsha, China

    Qilong Feng

  3. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, USA

    Jinhui Xu

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Guo, Z., Xiao, M., Zhou, Y. (2020). The Complexity of the Partition Coloring Problem. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_33

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  • DOI: https://doi.org/10.1007/978-3-030-59267-7_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59266-0

  • Online ISBN: 978-3-030-59267-7

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