Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

A New Proof for a Result of Kingan and Lemos’

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

Abstract

The prism graph is the planar dual of \(K_5 \backslash e\). Kingan and Lemos (Graphs Comb 30:1479–1497, 2014) proved a decomposition theorem for the class of binary matroids with no prism minor. In this paper, we present a different proof using fundamental graphs and blocking sequences.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bouchet, A., Cunningham, W.H., Geelen, J.F.: Principle unimodular skew-symmetric matrices. Combinatorica 18, 461–486 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Geelen, J.F., Gerards, A.M.H., Kapoor, A.: The excluded minors for \(GF(4)\)-representable matroids. J. Comb. Theory Ser. B 9, 247–299 (2001)

    MathSciNet  Google Scholar 

  3. Halfan, M.: Matroid Decomposition. Master’s essay, University of Waterloo (2002)

  4. Kingan, S.R., Lemos, M.: A decomposition theorem for binary matroids with no prism minor. Graphs Comb. 30(6), 1479–1497 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kingan, S.R., Lemos, M.: Strong Splitter Theorem. Ann. Comb. 18(1), 111–116 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  6. Oxley, J.G.: The binary matroids with no 4-wheel minor. Trans. Am. Math. Soc. 301, 663–679 (1987)

    Google Scholar 

  7. Oxley, J.G.: Matroid Theory. Oxford University Press, New York (1992)

    MATH  Google Scholar 

  8. Seymour, P.D.: Decomposition of regular matroids. J. Comb. Theory Ser. B 28, 305–359 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhou, X.: On internally 4-connected non-regular binary matroids. J. Comb. Theory Ser. B 91, 327–343 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiangqian Zhou.

Additional information

The authors wish to thank the anonymous referees for their constructive comments and very helpful suggestions. Dedicated to Dr. Neil Robertson on the occasion of his 75th birthday.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Williams, J.T., Zhou, X. A New Proof for a Result of Kingan and Lemos’. Graphs and Combinatorics 32, 403–417 (2016). https://doi.org/10.1007/s00373-015-1557-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-015-1557-y

Keywords

Navigation