Skip to main content
Log in

Cycle Covers of Planar 2-Edge-Connected Graphs

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

A graph with n vertices is said to have a small cycle cover provided its edges can be covered with at most (2n − 1)/3 cycles. Bondy [2] has conjectured that every 2-connected graph has a small cycle cover. In [3] Lai and Lai prove Bondy’s conjecture for plane triangulations. In [1] the author extends this result to all planar 3-connected graphs, by proving that they can be covered by at most (n + 1)/2 cycles. In this paper we show that Bondy’s conjecture holds for all planar 2-connected graphs. We also show that all planar 2-edge-connected graphs can be covered by at most (3n − 3)/4 cycles and we show an infinite family of graphs for which this bound is attained.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Barnette, D.W.: Cycle covers of planar 3-connected graphs. Journal of Combinatorial Mathematics and Combinatorial Computing (to be published)

  2. Bondy, J.A.: Small cycle double covers of graphs, Cycles and Rays. pp. 21–40. Dordecht: Kluwer Academic 1990

    Google Scholar 

  3. Lai, H.-J., Lai, H.: Cycle covering of plane triangulations. Journal of Combinatorial Mathematics and Combinatorial Computing 10, 3–12 (1991)

    MATH  MathSciNet  Google Scholar 

  4. Lai, H.-J.: Small cycle covers of planar graphs. Congress Numerantium (Proceedings for 1995 Southeastern Conference on Combinatorics, Graph Theory and Computing) (to be published)

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barnette, D.W. Cycle Covers of Planar 2-Edge-Connected Graphs. Graphs and Combinatorics 13, 315–323 (1997). https://doi.org/10.1007/BF03353010

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03353010

Keywords

Navigation