Skip to main content
SpringerLink
Log in

Cycles through four edges in 3-connected cubic graphs

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We give necessary and sufficient conditions for four edges in a 3-connected cubic graph to lie on a cycle. As a consequence, if such a graph is cyclically 4-edge-connected with order greater than 8 it is shown that any four independent edges lie on a cycle.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bussemaker, F.C., Cobeljic, S., Cvetkovic, D.M., Seidel, J.J.: Computer investigation of cubic graphs. Report 76-WSK-01. Eindhoven: Technological University 1976.

    MATH  Google Scholar 

  2. Ellingham, M.N., Holton, D.A., Little, C.H.C.: Cycles through ten vertices in 3-connected cubic graphs. Combinatorica (to appear)

  3. Häggvist, R., Thomassen, C.: Circuits through specified edges. Discrete Math.41, 29–34 (1982)

    Article  MathSciNet  Google Scholar 

  4. Holton, D.A., McKay, B.D., Plummer, M.D., Thomassen, C.: A nine point theorem for 3-connected graphs. Combinatorica2, 53–62 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Holton, D.A., Thomassen, C.: Research problem. Discrete Math. (to appear)

  6. Lovász, L.: Problem 5. Period. Math. Hung4, 82 (1974)

    Google Scholar 

  7. Thomassen, C.: Girth in graphs. J. Comb. Theory (B)35, 129–141 (1983)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, 3052, Parkville, Australia

    R. E. L. Aldred & D. A. Holton

  2. Mathematical Institute, The Technical University of Denmark, 2800, Lyngby, Denmark

    C. Thomassen

Authors
  1. R. E. L. Aldred
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Holton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Thomassen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was done while Thomassen was a visitor at the University of Melbourne. Support from the University of Melbourne, the Danish “Jubilæ and the Danish Science Research Council is greatfully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aldred, R.E.L., Holton, D.A. & Thomassen, C. Cycles through four edges in 3-connected cubic graphs. Graphs and Combinatorics 1, 7–11 (1985). https://doi.org/10.1007/BF02582923

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02582923

Keywords

Search

Navigation