Skip to main content
SpringerLink
Log in

An Algorithm for Cyclic Edge Connectivity of Cubic Graphs

(Extended Abstract)

  • Conference paper
Algorithm Theory - SWAT 2004 (SWAT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3111))

Included in the following conference series:

Abstract

The cyclic edge connectivity is the size of a smallest edge cut in a graph such that at least two of the connected components contain cycles. We present an algorithm running in time O(n 2log2 n) for computing the cyclic edge connectivity of n-vertex cubic graphs.

The REU programme where this research was originally started is supported by a cooperative research grant KONTAKT ME 521.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aldred, R.E.L., Holton, D.A., Jackson, B.: Uniform cyclic edge connectivity in cubic graphs. Combinatorica 11, 81–96 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Andersen, L.D., Fleischner, H., Jackson, B.: Removable edges in cyclically 4-edgeconnected cubic graphs. Graphs Comb. 4(1), 1–21 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  3. Caret, R.L., Dennistion, K.J., Topping, J.J.: Principles and applications of inorganic, organic & biological chemistry. C. Brown Publishers, Boston (1997)

    Google Scholar 

  4. Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Boston (1990)

    MATH  Google Scholar 

  5. Fleischner, H., Jackson, B.: A note concerning some conjectures on cyclically 4-edge connected 3-regular graphs. Ann. Disc. Math. 41, 171–177 (1989)

    Article  MathSciNet  Google Scholar 

  6. Lou, D., Teng, L., Wu, X.: A polynomial algorithm for cyclic edge connectivity of cubic graphs. Australasian J. Comb. 24, 247–259 (2001)

    MATH  MathSciNet  Google Scholar 

  7. Lou, D.: private communication

    Google Scholar 

  8. McCuaig, W.: Cycles through edges in cyclically k-connected cubic graphs. Discrete Math. 103 (1), 95–98 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. McCuaig, W.: Edge reductions in cyclically k-connected cubic graphs. J. Comb. Theory Ser. B 56 (1), 16–44 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Nedela, R., Škoviera, M.: Atoms of cyclic connectivity in cubic graphs. Math. Slovace 45, 481–499 (1995)

    MATH  Google Scholar 

  11. Nedela, R., Škoviera, M.: Decompositions and reductions of snarks. J. Graph Theory 22, 253–279 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Peroche, B.: On Several Sorts of Connectivity. Discrete Mathematics 46, 267–277 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  13. Plummer, M.D.: On the cyclic connectivity of planar graphs. In: Graph Theory and Applications, pp. 235–242. Springer, Heidelberg (1972)

    Chapter  Google Scholar 

  14. Tait, P.G.: Remarks on the colouring of maps. Proc. Roy. Soc. Edingburg 10, 501–503 (1880)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and, Institute for Theoretical Computer Science, Charles University, Malostranské náměstí 25, 118 00, Prague 1, Czech Republic

    Zdeněk Dvořák, Jan Kára, Daniel Král’ & Ondřej Pangrác

Authors
  1. Zdeněk Dvořák
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Kára
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Král’
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ondřej Pangrác
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Augsburg, 86135, Augsburg, Germany

    Torben Hagerup

  2. Department of Computing, University of Copenhagen, Denmark

    Jyrki Katajainen

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dvořák, Z., Kára, J., Král’, D., Pangrác, O. (2004). An Algorithm for Cyclic Edge Connectivity of Cubic Graphs. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27810-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22339-9

  • Online ISBN: 978-3-540-27810-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation