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International Computer Symposium

ICS 2018: New Trends in Computer Technologies and Applications pp 516–523Cite as

Total k-Domatic Partition and Weak Elimination Ordering

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1013))

Abstract

The total k-domatic partition problem is to partition the vertices of a graph into k pairwise disjoint total dominating sets. In this paper, we prove that the 4-domatic partition problem is NP-complete for planar graphs of bounded maximum degree. We use this NP-completeness result to show that the total 4-domatic partition problem is also NP-complete for planar graphs of bounded maximum degree. We also show that the total k-domatic partition problem is linear-time solvable for any bipartite distance-hereditary graph by showing how to compute a weak elimination ordering of the graph in linear time. The linear-time algorithm for computing a weak elimination ordering of a bipartite distance-hereditary graph can lead to improvement on the complexity of several graph problems or alternative solutions to the problems such as signed total domination, minus total domination, k-tuple total domination, and total \(\{k\}\)-domination problems.

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Notes

  1. 1.

    The graph is modified from [6].

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Acknowledgment

The work is supported by an internal research project of Ming Chuan University (2018/11/1–2019/3/31) and partially supported by Research Grant: MOST-106-2221-E-130-006 in Taiwan. The author is grateful to the anonymous referees for their valuable comments and suggestions to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Computer and Communication Engineering, Ming Chuan University, 5 De Ming Rd., Guishan District, Taoyuan City 333, Taiwan

    Chuan-Min Lee

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  1. Chuan-Min Lee
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Correspondence to Chuan-Min Lee .

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Editors and Affiliations

  1. National Yunlin University of Science and Technology, Douliu, Taiwan

    Chuan-Yu Chang

  2. National Yunlin University of Science and Technology, Douliu, Taiwan

    Chien-Chou Lin

  3. Southern Taiwan University of Science and Technology, Tainan, Taiwan

    Horng-Horng Lin

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Lee, CM. (2019). Total k-Domatic Partition and Weak Elimination Ordering. In: Chang, CY., Lin, CC., Lin, HH. (eds) New Trends in Computer Technologies and Applications. ICS 2018. Communications in Computer and Information Science, vol 1013. Springer, Singapore. https://doi.org/10.1007/978-981-13-9190-3_57

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  • DOI: https://doi.org/10.1007/978-981-13-9190-3_57

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9189-7

  • Online ISBN: 978-981-13-9190-3

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