On the complexity of the maximum cut problem

  • Hans L. Bodlaender
  • Klaus Jansen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


The complexity of the SIMPLE MAXCUT problem is investigated for several special classes of graphs. It is shown that this problem is NP-complete when restricted to one of the following classes: chordal graphs, undirected path graphs, split graphs, tripartite graphs, and graphs that are the complement of a bipartite graph. The problem can be solved in polynomial time, when restricted to graphs with bounded treewidth, or cographs. We also give large classes of graphs that can be seen as generalizations of classes of graphs with bounded treewidth and of the class of the cographs, and allow polynomial time algorithms for the SIMPLE MAX CUT problem.


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  1. 1.
    Arnborg, S.: Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey. BIT 25 (1985) 2–23.Google Scholar
  2. 2.
    Bodlaender, H.L.: Achromatic Number is NP-complete for cographs and interval graphs. Information Processing Letters 31 (1989) 135–138.Google Scholar
  3. 3.
    Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. In: Proceedings of the 25th Annual Symposium on Theory of Computing, pages 226–234. ACM Press, 1993.Google Scholar
  4. 4.
    Bodlaender, H.L.: A tourist guide through treewidth. Technical Report RUU-CS-92-12, Department of Computer Science, Utrecht University, Utrecht, 1992. To appear in: Acta Cybernetica.Google Scholar
  5. 5.
    Chang, K., Du, D.: Efficient algorithms for the layer assignment problem. IEEE Trans. CAD 6 (1987) 67–78.Google Scholar
  6. 6.
    Chen, R., Kajitani, Y., Chan, S.: A graph theoretic via minimization algorithm for two layer printed circuit boards. IEEE Trans. Circuit Syst. (1983) 284–299.Google Scholar
  7. 7.
    Corneil, D.G., Perl, Y., Stewart, L.K.: A linear recognition algorithm for cographs. SIAM J. Comput. 4 (1985) 926–934.Google Scholar
  8. 8.
    Földes, S., Hammer, P.L.: Split graphs. In: Proceedings of the 8th Southeastern Conf. on Combinatorics, Graph Theory and Computing, pages 311–315. Louisiana State University, Baton Rouge, Louisiana, 1977.Google Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, 1979.Google Scholar
  10. 10.
    Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete graph problems. Theoretical Computer Science 1 (1976) 237–267.Google Scholar
  11. 11.
    Jansen, K., Scheffler, P.: Some coloring results for tree like graphs. Workshop on Graph Theoretic Concepts in Computer Science. LNCS 657 (1992) 50–59.Google Scholar
  12. 12.
    Johnson, D.S.: The NP-completeness column: an ongoing guide. J. Algorithms 6 (1985) 434–451.Google Scholar
  13. 13.
    Karp, R.M.: Reducibility among combinatorial problems. in: Miller and Thatcher (eds.): Complexity of Computer Computations, Plenum Press (1972) 85–104.Google Scholar
  14. 14.
    Muller, J.M., Spinrad, L.: Incremental modular decomposition. J. ACM. 36 (1989) 1–19.Google Scholar
  15. 15.
    Pinter, R.: Optimal layer assignment for interconnect. In: Proc. Int. Symp. Circuit Syst. (ISCAS) (1982) 398–401.Google Scholar
  16. 16.
    Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms 7 (1986) 309–322.Google Scholar
  17. 17.
    Trotter, W.T.Jr., Harary, F.: On double and multiple interval graphs. J. Graph Theory 3 (1979) 205–211.Google Scholar
  18. 18.
    Wanke, E.: k-NLC graphs and polynomial algorithms. Bericht. Reihe Informatik 80. Universität Paderborn, 1991.Google Scholar
  19. 19.
    Wimer, T.V.: Linear algorithms on k-terminal graphs. PhD thesis. Department of Computer Science. Clemson University, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Klaus Jansen
    • 2
  1. 1.Department of Computer ScienceUtrecht UniversityTB UtrechtThe Netherlands
  2. 2.Fachbereich 11 - Mathematik, FG InformatikUniversität DuisburgDuisburgGermany

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