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Algorithms for finding f-colorings of partial k-trees

An extended abstract
  • Xiao Zhou
  • Takao Nishizeki
Session 10
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1004)

Abstract

In an ordinary edge-coloring of a graph G=(V, E) each color appears at each vertex v ∈ V at most once. An f-coloring is a generalized edge-coloring in which each color appears at each vertex v ∈ V at most f(v) times, where f(v) is a positive integer assigned to v. This paper gives a linear-time sequential algorithm and an optimal parallel algorithm which find an f-coloring of a givenpartial k-tree with the minimum number of colors.

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References

  1. 1.
    H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. In Proc. of the 25th Ann. ACM Symp. on Theory of Computing, pp. 226–234, San Diego, CA, 1993.Google Scholar
  2. 2.
    R. B. Borie, R. G. Parker, and C. A. Tovey. Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families. Algorithmica, 7, pp. 555–581, 1992.Google Scholar
  3. 3.
    S. Fiorini and R. J. Wilson. Edge-Colourings of Graphs. Pitman, London, 1977.Google Scholar
  4. 4.
    A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge Univ. Press, Cambridge, 1988.Google Scholar
  5. 5.
    S. L. Hakimi and O. Kariv. On a generalization of edge-coloring in graphs. Journal of Graph Theory, 10, pp. 139–154, 1986.Google Scholar
  6. 6.
    I. Holyer. The NP-completeness of edge-colouring. SIAM J. Comput., 10, pp. 718–720, 1981.Google Scholar
  7. 7.
    J. JáJá. An Introduction to Parallel Algorithms. Addison-Wesley, New York, 1992.Google Scholar
  8. 8.
    S. Nakano and T. Nishizeki. Scheduling file transfers under port and channel constraints. Int. J. Found. of Comput. Sci., 4(2), pp. 101–115, 1993.Google Scholar
  9. 9.
    T. Nishizeki and N. Chiba. Planar Graphs: Theory and Algorithms. North-Holland, Amsterdam, 1988.Google Scholar
  10. 10.
    B.A. Reed. Finding approximate separators and computing tree-width quickly. In Proc. of the 24th Ann. ACM Symp. on Theory of Computing, pp. 221–228, 1992.Google Scholar
  11. 11.
    V. G. Vizing. On an estimate of the chromatic class of a p-graph. Discret Analiz, 3, pp. 25–30, 1964.Google Scholar
  12. 12.
    X. Zhou, S. Nakano, and T. Nishizeki. A linear algorithm for edge-coloring partial k-trees. In Proc. of the First Europian Symposium on Algorithms, Lect. Notes in Computer Science, Springer-Verlag, 726, pp. 409–418, 1993.Google Scholar
  13. 13.
    X. Zhou, S. Nakano, and T. Nishizeki. A parallel algorithm for edge-coloring partial k-trees. In Proc. of the Fourth Scandinavian Workshop on Algorithm Theory, Lect. Notes in Computer Science, Springer-Verlag, 824, pp. 359–369, 1994.Google Scholar
  14. 14.
    X. Zhou and T. Nishizeki. Optimal parallel algorithms for edge-coloring partial k-trees with bounded degrees. IEICE Trans. on Fundamentals of Electronics, Communication and Computer Sciences, E78-A, pp. 463–469, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Xiao Zhou
    • 1
  • Takao Nishizeki
    • 2
  1. 1.Education Center for Information ProcessingTohoku UniversitySendaiJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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