Skip to main content
Log in

A linear time algorithm for computing 3-edge-connected components in a multigraph

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

This paper presents a linear time algorithm for computing all 3-edge-connected components in a given multigraph.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A.H. Esfahanian and S.L. Hakimi, On computing the connectivities of graphs and digraphs. Networks,14 (1984), 355–366.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Eswaran and R.E. Tarjan, Augmentation problems. SIAM J. Comput.,5 (1976), 653–665.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Even and R.E. Tarjan, Network flow and testing graph connectivity. SIAM J. Comput.,4 (1975), 507–518.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Frank, T. Ibaraki and H. Nagamochi, On sparse subgraphs preserving connectivity properties. Preprint, 1991.

  5. H.N. Gabow, A matroid approach to finding edge connectivity and packing arborescences. Proc. 23rd ACM Symp. on Theory of Computing, 1991, 112–122.

  6. Z. Galil, Finding the vertex connectivity of graphs. SIAM J. Comput.,9 (1980), 197–199.

    Article  MATH  MathSciNet  Google Scholar 

  7. Z. Galil and G.F. Italiano, reducing edge connectivity to vertex connectivity. SIGACT News,22 (1991), 57–61.

    Article  Google Scholar 

  8. J. Hopcroft and R.E. Tarjan, Dividing a graph into triconnected components. SIAM J. Comput.,2 (1973), 135–158.

    Article  MathSciNet  Google Scholar 

  9. A.V. Karzanov and E.A. Timofeev, Efficient algorithm for finding all minimal edge cuts of a nonoriented graph. Kibernetika,2 (1986), 8–12; translated in Cybernetics,2 (1986), 156–162.

    MathSciNet  Google Scholar 

  10. D.W. Matula, Determining edge connectivity inO(nm). Proc. 28th IEEE Symp. Found. Compt. Sci., 1987, 249–251.

  11. D.W. Matula, A linear time 2+ɛ approximation algorithm for edge connectivity. Preprint 14, Institut for Matematik og Datalogi, Odense Univ., 1990.

  12. H. Nagamochi and T. Ibaraki, Linear time algorithm for finding a sparsek-connected spanning subgraph of ak-connected graph. Algorithmica,7 (1992), 583–596.

    Article  MATH  MathSciNet  Google Scholar 

  13. N. Nagamochi and T. Ibaraki, Computing edge-connectivity in multigraphs and capacitated graphs. SIAM J. Discrete Math.,5 (1992), 54–66.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. Nagamochi and T. Ibaraki, A linear time algorithm for computing 3-edge-connected components of a multigraph. Technical Report #91005, Department of Applied Mathematics and Physics, Kyoto Univ., 1991.

  15. H. Nagamochi, Z. Sun and T. Ibaraki, Counting the number of minimum cuts in undirected multigraphs. IEEE Trans. Reliability,40 (1991), 610–614.

    Article  MATH  Google Scholar 

  16. H. Nagamochi and T. Watanabe, Computingk-edge connected components of a multigraph. IEICE, Technical Report COMP90-94, 1991, 33–38.

  17. T. Nishizeki and S. Poljak,k-connectivity and decomposition of graphs into forests. Discrete Appl. Math. (to appear).

  18. C.P. Schnorr, Bottlenecks and edge connectivity in unsymmetrical networks. SIAM J. Comput.,8 (1979), 265–274.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. Taoka, T. Watanabe and K. Onaga, Computing all 3-edge-components of an undirected multigraph in linear time. Report 91-AL-21-5, SIG Algorithms, Information Processing Soc. Japan, 1991.

  20. R.E. Tarjan, Depth-first search and linear graph algorithms. SIAM J. Comput.,1 (1972), 146–160.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Nagamochi, H., Ibaraki, T. A linear time algorithm for computing 3-edge-connected components in a multigraph. Japan J. Indust. Appl. Math. 9, 163 (1992). https://doi.org/10.1007/BF03167564

Download citation

  • Received:

  • DOI: https://doi.org/10.1007/BF03167564

Key words

Navigation