Skip to main content
Springer Nature Link
Log in

Generating Minimal k-Vertex Connected Spanning Subgraphs

  • Conference paper
Computing and Combinatorics (COCOON 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4598))

Included in the following conference series:

Abstract

We show that minimal k-vertex connected spanning subgraphs of a given graph can be generated in incremental polynomial time for any fixed k.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Tamura, A., Shioura, A., Uno, T.: An optimal algorithm for scanning all spanning trees of undirected graphs. SIAM Journal on Computing 26(3), 678–692 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berge, C.: Hypergraphs. Elsevier-North Holland, Amsterdam (1989)

    Book  MATH  Google Scholar 

  3. Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L.: Generating maximal independent sets for hypergraphs with bounded edge-intersections. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 488–498. Springer, Heidelberg (2004)

    Google Scholar 

  4. Cheriyan, J., Kao, M.-Y., Thurimella, R.: Algorithms for parallel k-vertex connectivity and sparse certificates. 22, 157–174 (1993)

    Google Scholar 

  5. Coulbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, Oxford (1987)

    Google Scholar 

  6. Gabow, H.N., Myers, E.W.: Finding all spanning trees of directed and undirected trees. SIAM Journal on Computing 117, 280–287 (1978)

    Article  MathSciNet  Google Scholar 

  7. Johnson, D.S., Papadimitriou, Ch.H.: On generating all maximal independent sets. Information Processing Letters 27, 119–123 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Khachiyan, L., Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Makino, K.: Enumerating spanning and connected subsets in graphs and matroids. Manuscript.

    Google Scholar 

  9. Khachiyan, L., Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Makino, K.: Generating cut conjunctions and bridge avoiding extensions in graphs. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 156–165. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Lawler, E., Lenstra, J.K., Kan, A.H.G.R.: Generating all maximal independent sets: NP-hardness and polynomial-time algorithms. SIAM Journal on Computing 9, 558–565 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  11. Matsui, T.: Algorithms for finding all the spanning trees in undirected graphs. Technical report, Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo, Report METR93-08 (1993)

    Google Scholar 

  12. Read, R.C., Tarjan, R.E.: Bounds on backtrack algorithms for listing cycles, paths, and spanning trees. Networks 5, 237–252 (1975)

    MATH  MathSciNet  Google Scholar 

  13. Schwikowski, B., Speckenmeyer, E.: On enumerating all minimal solutions of feedback problems. Discrete Applied Mathematics 117, 253–265 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Valiant, L.: The complexity of enumeration and reliability problems. SIAM Journal on Computing 8, 410–421 (1979)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway NJ 08854-8003,  

    Endre Boros, Konrad Borys, Vladimir Gurvich & Gabor Rudolf

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Khaled Elbassioni

  3. Division of Mathematical Science for Social Systems, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Kazuhisa Makino

Authors
  1. Endre Boros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Konrad Borys
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Khaled Elbassioni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vladimir Gurvich
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kazuhisa Makino
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Gabor Rudolf
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Guohui Lin

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Makino, K., Rudolf, G. (2007). Generating Minimal k-Vertex Connected Spanning Subgraphs. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73545-8_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73544-1

  • Online ISBN: 978-3-540-73545-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics