Maximum Connected Domatic Partition of Directed Path Graphs with Single Junction

  • Masaya Mito
  • Satoshi Fujita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


In this paper, we consider the problem of finding a maximum connected domatic partition of a given graph. We propose a polynomial time algorithm for solving the problem for a subclass of directed path graphs which is known as a class of intersection graphs modeled by a set of directed paths on a directed tree. More specifically, we restrict the class of directed path graphs in such a way that the underlying directed tree has at most one node to have several incoming arcs.


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  1. 1.
    Bertossi, A.A.: On the Domatic Number of Interval Graphs. Information Processing Letters 28(6), 275–280 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bonuccelli, M.A.: Dominating Sets and Domatic Number of Circular Arc Graphs. Discrete Applied Mathematics 12, 203–213 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    CardeiM, M., Du, D.-Z.: Improving Wireless Sensor Network Lifetime through Power Aware Organization. ACM Wireless Networks 11(3), 333–340 (2005)CrossRefGoogle Scholar
  4. 4.
    Cole, R., Ost, K., Schirra, S.: Edge-Coloring Bipartite Multigraphs in O(E logD) Time. Combinatorica 21(1), 5–12 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dai, F., Wu, J.: An Extended Localized Algorithm for Connected Dominating Set Formation in Ad Hoc Wireless Networks. IEEE Transactions on Parallel and Distributed Systems 53(10), 1343–1354 (2004)Google Scholar
  6. 6.
    Dong, Q.: Maximizing System Lifetime in Wireless Sensor Networks. In: Proc. of the 4th International Symposium on Information Processing in Sensor Networks, pp. 13–19 (2005)Google Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979)zbMATHGoogle Scholar
  8. 8.
    Guha, S., Khuller, S.: Approximation Algorithms for Connected Dominating Sets. In: Proc. European Symposium on Algorithms, pp. 179–193 (1996)Google Scholar
  9. 9.
    Ha, R.W., Ho, P.H., Shen, X., Zhang, J.: Sleep Scheduling for Wireless Sensor Networks via Network Flow Model. Computer Communications 29(13-14), 2469–2481 (2006)CrossRefGoogle Scholar
  10. 10.
    Hartnell, B.L., Rall, D.F.: Connected Domatic Number in Planar Graphs. Czechoslovak Mathematical Journal 51(1), 173–179 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)zbMATHGoogle Scholar
  12. 12.
    Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Domination in Graphs: Advanced Topics. Marcel Dekker, New York (1998)zbMATHGoogle Scholar
  13. 13.
    Hedetniemi, S., Laskar, R.: Connected domination in Graphs. In: Graph Theory and Combinatorics, pp. 209–218. Academic Press, London (1984)Google Scholar
  14. 14.
    Wu, J., Li, H.: Domination and Its Applications in Ad Hoc Wireless Networks with Unidirectional Links. In: Proc. of International Conference on Parallel Processing, pp. 189–200 (2000)Google Scholar
  15. 15.
    Wu, J.: Extended Dominating-Set-Based Routing in Ad Hoc Wireless Networks with Unidirectional Links. IEEE Transactions on Parallel and Distributed Computing 22, 327–340 (2002)Google Scholar
  16. 16.
    Zelinka, B.: Connected Domatic Number of a Graph. Math. Slovaca 36, 387–392 (1986)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Masaya Mito
    • 1
  • Satoshi Fujita
    • 1
  1. 1.Department of Information Engineering Graduate School of EngineeringHiroshima University 

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