Finding all minimal separators of a graph

  • T. Kloks
  • D. Kratsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


In this paper we give an efficient algorithm to find all minimal vertex separators of an undirected graph. The algorithm needs polynomial time per separator that is found.


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  1. 1.
    Arnborg, S., Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey, BIT 25, (1985), pp. 2–23.Google Scholar
  2. 2.
    Arnborg, S., J. Lagergren and D. Seese, Easy problems for tree-decomposable graphs, J. Algorithms 12, (1991), pp. 308–340.Google Scholar
  3. 3.
    Arnborg, S. and A. Proskurowski, Linear time algorithms for NP-hard problems restricted to partial k-trees, Disc. Appl. Math. 23, (1989), pp. 305–314.Google Scholar
  4. 4.
    Bodlaender, H., A tourist guide through treewidth, Technical report RUU-CS-92-12, Department of Computer Science, Utrecht University, Utrecht, The Netherlands, (1992).Google Scholar
  5. 5.
    Bodlaender, H., A linear time algorithm for finding tree-decompositions of small treewidth, Proceedings of the 25th Annual ACM Symposium on Theory of Computing, (1993), pp. 226–234.Google Scholar
  6. 6.
    Bodlaender, H., T. Kloks and D. Kratsch, Treewidth and pathwidth of permutation graphs, Proceedings of the 20th International Colloquium on Automata, Languages and Programming, Springer-Verlag, Lecture Notes in Computer Science 700, (1993), pp. 114–125.Google Scholar
  7. 7.
    Gavril, F., Algorithms on clique separable graphs, Discrete Math. 19 (1977), pp. 159–165.Google Scholar
  8. 8.
    Goldberg, L. A., Efficient algorithms for listing combinatorial structures, Cambridge University press, 1993.Google Scholar
  9. 9.
    Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.Google Scholar
  10. 10.
    Kanevsky, A., On the number of minimum size separating vertex sets in a graph and how to find all of them, Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 411–421, (1990).Google Scholar
  11. 11.
    Kloks, T., Treewidth, Ph.D. Thesis, Utrecht University, The Netherlands, 1993.Google Scholar
  12. 12.
    Kloks, T., Treewidth of circle graphs, To appear in: proceedings ISAAC'94.Google Scholar
  13. 13.
    Kloks, T. and D. Kratsch, Treewidth of chordal bipartite graphs, 10th Annual Symposium on Theoretical Aspects of Computer Science, Springer-Verlag, Lecture Notes in Computer Science 665, (1993), pp. 80–89.Google Scholar
  14. 14.
    Kloks, T., Minimum fill-in for chordal bipatite graphs, Technical report RUU-CS-93-11, Department of Computer Science, Utrecht University, Utrecht, The Netherlands, (1993).Google Scholar
  15. 15.
    Tarjan, R. E., Decomposition by clique separators, Discrete Mathematics 55 (1985), pp. 221–232.Google Scholar
  16. 16.
    Whitesides, S. H., An Algorithm for finding clique cut-sets, Information Processing Letters 12 (1981), pp. 31–32.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • T. Kloks
    • 1
  • D. Kratsch
    • 2
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyMB EindhovenThe Netherlands
  2. 2.Fakultät für Mathematik und InformatikFriedrich-Schiller-UniversitätJenaGermany

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