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An efficient algorithm for edge-coloring series parallel multigraphs

  • X. Zhou
  • S. Nakano
  • H. Suzuki
  • T. Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 583)

Abstract

Many combinatorial problems can be efficiently solved for series-parallel graphs or partial k-trees. The edge-coloring problem is one of a few combinatorial problems for which no efficient algorithms have been obtained for series-parallel multigraphs. This paper gives an algorithm which optimally edge-colors a given series-parallel multigraph in time OV¦Δ), where V is the set of vertices and Δ the maximum degree.

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References

  1. [ACPD]
    S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese, An algebraic theory of graph reduction, Tech. Rept. 91-36, Laboratoire Bordelais de Recherche en Informatique, Bordeaux, 1991.Google Scholar
  2. [AL]
    S. Arnborg and J. Lagergren, Easy problems for tree-decomposable graphs, Journal of Algorithms, 12, 2, pp.308–340, 1991.Google Scholar
  3. [B]
    H. L. Bodlaender. Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees, Journal of Algorithms, 11, 4, pp.631–643, 1990.Google Scholar
  4. [C]
    B. Courcelle, The monadic second-order logic of graphs I: Recognizable sets of finite graphs, Information and Computation, 85, pp.12–75, 1990.Google Scholar
  5. [Sey]
    P. D. Seymour, Colouring series-parallel graphs, Combinatorica 10(4), PP-379–392, 1990.Google Scholar
  6. [Sys]
    M. Sysło, NP-complete problems on some tree-structured graphs: a review, In M. Nagl and J. Perl, editors, Proc. WG'83 International Workshop on Graph Theoretic Concepts in Comouter Science, pp. 342–353, Univ. Verlag Rudolf Trauner, Linz, West Germany, 1983.Google Scholar
  7. [TN]
    O. Terada and T. Nishizeki, Approximate algorithms for the edge-coloring of graphs, Trans. Inst, of Electronics and Communication Eng. of Japan, J65-D, 11, pp. 1382–1389, 1982.Google Scholar
  8. [TNS]
    K. Takamizawa, T. Nishizeki, and N. Saito, Linear-time computability of combinatorial problems on series-parallel graphs, J. of ACM, 29, 3, pp. 623–641, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • X. Zhou
    • 1
  • S. Nakano
    • 1
  • H. Suzuki
    • 1
  • T. Nishizeki
    • 1
  1. 1.Department of Information Engineering, Faculty of EngineeringTohoku UniversityJapan

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