Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1991: Graph-Theoretic Concepts in Computer Science pp 230–238Cite as

On disjoint cycles

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 570))

Abstract

It is shown, that for each constant k ≥ 1, the following problems can be solved in O(n) time: given a graph G, determine whether G has k vertex disjoint cycles, determine whether G has k edge disjoint cycles, determine whether G has a feedback vertex set of size ≤ k. Also, every class \(\mathcal{G}\), that is closed under minor taking, or that is closed under immersion taking, and that does not contain the graph formed by taking the disjoint union of k copies of K 3, has an \(\mathcal{O}\)(n) membership test algorithm.

This work has been partially supported by the ESPRIT II Basic Research Actions Program of the EC, under contract No. 3075 (project ALCOM).

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey. BIT, 25:2–23, 1985.

    Google Scholar 

  2. S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese. An algebraic theory of graph reduction. Technical Report 90-02, Laboratoire Bordelais de Recherche en Informatique, Bordeaux, 1990. To appear in Proceedings 4th Workshop on Graph Grammars and Their Applications to Computer Science.

    Google Scholar 

  3. S. Arnborg, J. Lagergren, and D. Seese. Problems easy for tree-decomposable graphs (extended abstract). In Proceedings of the 15'th International Colloquium on Automata, Languages and Programming, pages 38–51. Springer Verlag, Lect. Notes in Comp. Sc. 317, 1988. To appear in J. of Algorithms.

    Google Scholar 

  4. H. L. Bodlaender. Classes of graphs with bounded treewidth. Technical Report RUU-CS-86-22, Dept. of Computer Science, Utrecht University, Utrecht, 1986.

    Google Scholar 

  5. H. L. Bodlaender. NC-algorithms for graphs with small treewidth. In J. van Leeuwen, editor, Proc. Workshop on Graph-Theoretic Concepts in Computer Science WG'88, pages 1–10. Springer Verlag, LNCS 344, 1988.

    Google Scholar 

  6. H. L. Bodlaender. On linear time minor tests and depth first search. In Proceedings Workshop on Algorithms and Data Structures WADS'89, pages 577–590. Springer Verlag, Lecture Notes in Computer Science, vol. 382, 1989.

    Google Scholar 

  7. R. B. Borie, R. G. Parker, and C. A. Tovey. Automatic generation of linear algorithms from predicate calculus descriptions of problems on recursive constructed graph families. Manuscript, 1988.

    Google Scholar 

  8. D. J. Brown, M. R. Fellows, and M. A. Langston. Nonconstructive polynomial-time decidability and self-reducibility. Int. J. Computer Math., 31:1–9, 1989.

    Google Scholar 

  9. P. Erdös and G. Szekeres. A combinatorial problem in geometry. Compos. Math., 2:464–470, 1935.

    Google Scholar 

  10. M. R. Fellows, 1989. Personal communication.

    Google Scholar 

  11. M. R. Fellows and M. A. Langston. On search, decision and the efficiency of polynomial-time algorithms. In Proceedings of the 21th Annual Symposium on Theory of Computing, pages 501–512, 1989.

    Google Scholar 

  12. M. R. Garey and D. S. Johnson. Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York, 1979.

    Google Scholar 

  13. J. Lagergren. Efficient parallel algorithms for tree-decomposition and related problems. In Proceedings of the 31th Annual Symposium on Foundations of Computer Science, pages 173–182, 1990.

    Google Scholar 

  14. N. Robertson and P. D. Seymour. Graph minors. XV. Wagner's conjecture. To appear.

    Google Scholar 

  15. N. Robertson and P. D. Seymour. Graph minors — a survey. In I. Anderson, editor, Surveys in Combinatorics, pages 153–171. Cambridge Univ. Press, 1985.

    Google Scholar 

  16. N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. Manuscript, 1986.

    Google Scholar 

  17. J. van Leeuwen. Graph algorithms. In Handbook of Theoretical Computer Science, A: Algorithms and Complexity Theory, Amsterdam, 1990. North Holland Publ. Comp.

    Google Scholar 

  18. T. V. Wimer. Linear algorithms on k-terminal graphs. PhD thesis, Dept. of Computer Science, Clemson University, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Utrecht, P.O.Box 80.089, 3508, TB Utrecht, The Netherlands

    Hans L. Bodlaender

Authors
  1. Hans L. Bodlaender
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Gunther Schmidt Rudolf Berghammer

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bodlaender, H.L. (1992). On disjoint cycles. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-55121-2_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55121-8

  • Online ISBN: 978-3-540-46735-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation