Skip to main content
SpringerLink
Log in

Strong 5-Cycle Double Covers of Graphs

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

The Cycle Double Cover Conjecture claims that every bridgeless graph has a cycle double cover and the Strong Cycle Double Conjecture states that every such graph has a cycle double cover containing any specified circuit. In this paper, we get a necessary and sufficient condition for bridgeless graphs to have a strong 5-cycle double cover. Similar condition for the existence of 5-cycle double covers is also obtained. These conditions strengthen/improve some known results.

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. Celmins, U.A.: On Cubic Graphs That do not have an Edge 3-Coloring, Ph.D. Thesis, University of Waterloo (1984)

  2. Fleischner, H.: Cycle decompositions, 2-coverings, removable cycles and the four-color disease. In: Bondy, J.A., Murty, U.S.R. (eds.): Progress in Graph Theory, pp. 233–246. Academic Press, New York (1984)

  3. Fleischner H.: Proof of the strong 2-cover conjecture for planar graphs. J. Combin. Theory Ser. B 40, 229–230 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  4. Goddyn, L.: Cycle Covers of Graphs, Ph.D. Thesis, University of Waterloo (1988)

  5. Hoffmann-Ostenhof, A.: A note on 5-cycle double covers. Graphs Combin. doi:10.1007/s00373-012-1169-8

  6. Hoffmann-Ostenhof, A.: http://garden.irmacs.sfu.ca/?q=op/strong_5_cycle_double_cover_conjecture. August 3rd, 2010

  7. Preissmann, M.: Sur les Colorations des Arêtes des Graphs Cubiques, Thèse de Doctorat de 3eme, Grenoble (1981)

  8. Seymour, P.D.: Sums of circuits. In: Bondy, J.A., Murty, U.R.S. (eds.) Graph Theory and Related Topics. Academic Press, New York, pp. 342–355 (1979)

  9. Szekeres G.: Polyhedral decompositions of cubic graphs. Bull. Austral. Math. Soc. 8, 367–387 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  10. Zhang C.Q.: Nowhere-zero 4-flows and cycle double covers. Discrete Math. 154, 245–253 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhang, C.-Q.: Integer Flows and Cycle Covers of Graphs. Marcel Dekker, New York (1997)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of West Georgia, Carrollton, GA, 30118, USA

    Rui Xu

Authors
  1. Rui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rui Xu.

Additional information

Research is partially supported by the 2011-2012 COSM Research Incentive Award of UWG.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, R. Strong 5-Cycle Double Covers of Graphs. Graphs and Combinatorics 30, 495–499 (2014). https://doi.org/10.1007/s00373-012-1266-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-012-1266-8

Keywords

Search

Navigation