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IFIP International Conference on Theoretical Computer Science

TCS 2012: Theoretical Computer Science pp 240–249Cite as

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The Algorithmic Complexity of k-Domatic Partition of Graphs

The Algorithmic Complexity of k-Domatic Partition of Graphs

  • Hongyu Liang18 
  • Conference paper
  • 832 Accesses

  • 1 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7604)

Abstract

Let G = (V,E) be a simple undirected graph, and k be a positive integer. A k-dominating set of G is a set of vertices S ⊆ V satisfying that every vertex in V ∖ S is adjacent to at least k vertices in S. A k-domatic partition of G is a partition of V into k-dominating sets. The k-domatic number of G is the maximum number of k-dominating sets contained in a k-domatic partition of G. In this paper we study the k-domatic number from both algorithmic complexity and graph theoretic points of view. We prove that it is \(\mathcal{NP}\)-complete to decide whether the k-domatic number of a bipartite graph is at least 3, and present a polynomial time algorithm that approximates the k-domatic number of a graph of order n within a factor of \((\frac{1}{k}+o(1))\ln n\), generalizing the (1 + o(1))ln n approximation for the 1-domatic number given in [5]. In addition, we determine the exact values of the k-domatic number of some particular classes of graphs.

Keywords

  • Sensor Network
  • Bipartite Graph
  • Polynomial Time Algorithm
  • Algorithmic Complexity
  • Domination Number

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, and the National Natural Science Foundation of China Grant 61033001, 61061130540, 61073174.

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Author information

Authors and Affiliations

  1. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Hongyu Liang

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  1. Hongyu Liang
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Editors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Jos C. M. Baeten & Frank S. de Boer & 

  2. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Tom Ball

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Liang, H. (2012). The Algorithmic Complexity of k-Domatic Partition of Graphs. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_17

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