Advertisement

How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time

  • Wolfgang Espelage
  • Frank Gurski
  • Egon Wanke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2204)

Abstract

We show that many non-MSO1 NP-hard graph problems can be solved in polynomial time on clique-width and NLC-width bounded graphs using a very general and simple scheme. Our examples are partition into cliques, partition into triangles, partition into complete bipartite subgraphs, partition into perfect matchings, partition into forests, cubic subgraph, Hamiltonian path, minimum maximal matching, and vertex/edge separation problems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.G. Corneil, M. Habib, J.M. Lanlignel, B. Reed, and U. Rotics. Polynomial time recognition of clique-width at most three graphs. In Proceedings of Latin American Symposium on Theoretical Informatics (LATIN’ 2000), volume 1776 of LNCS. Springer-Verlag, 2000.CrossRefGoogle Scholar
  2. 2.
    B. Courcelle, J.A. Makowsky, and U. Rotics. Linear time solvable optimization problems on graphs of bounded clique width. Theory of Computing Systems, 33(2):125–150, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Courcelle and S. Olariu. Upper bounds to the clique width of graphs. Discrete Applied Mathematics, 101:77–114, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    D.G. Corneil, Y. Perl, and L.K. Stewart. A linear recognition algorithm for cographs. SIAM Journal on Computing, 14(4):926–934, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    D.G. Corneil and U. Rotics. On the relationship between clique-width and treewidth. In Proceedings of Graph-Theoretical Concepts in Computer Science, LNCS, Springer-Verlag, 2001. to appearGoogle Scholar
  6. 6.
    M.C. Golumbic and U. Rotics. On the clique-width of perfect graph classes. IJFCS: International Journal of Foundations of Computer Science, 11(3):423–443, 2000.CrossRefMathSciNetGoogle Scholar
  7. 7.
    F. Gurski and E. Wanke. The tree-width of clique-width bounded graphs without K n,n. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1938 of LNCS, pages 196–205. Springer-Verlag, 2000.CrossRefGoogle Scholar
  8. 8.
    Ö. Johansson. Clique-decomposition, NLC-decomposition, and modular decomposition — relationships and results for random graphs. Congressus Numerantium, 132:39–60, 1998.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ö. Johansson. NLC2 decomposition in polynomial time. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1665 of LNCS, pages 110–121. Springer-Verlag, 1999.CrossRefGoogle Scholar
  10. 10.
    D. Kobler and U. Rotics. Polynomial algorithms for partitioning problems on graphs with fixed clique-width. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pages 468–476 ACM-SIAM, 2001.Google Scholar
  11. 11.
    E. Wanke. k-NLC graphs and polynomial algorithms. Discrete Applied Mathematics, 54:251–266, 1994. Revised version, “http://www.cs.uniduesseldorf.de/~wanke”.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Wolfgang Espelage
    • 1
  • Frank Gurski
    • 1
  • Egon Wanke
    • 1
  1. 1.Department of Computer ScienceDüsseldorfGermany

Personalised recommendations