Skip to main content
SpringerLink
Log in

The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle

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

Abstract

A graph is said to be k-extendable if any independent set of k edges extends to a perfect matching. We shall show that every 5-connected graph of even order embedded on the projective plane and every 6-connected one embedded on the torus and the Klein bottle is 2-extendable and characterize the forbidden structures for 5-connected toroidal graphs to be 2-extendable.

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. Aldred R.E.L., Kawarabayashi K., Plummer M.D.: On the matching extendability of graphs in surfaces. J. Combin. Theory. Ser B. 98, 105–115 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dean N.: The matching extendability of surfaces. J. Combin. Theory. Ser. B. 54, 133–141 (1992)

    Article  MathSciNet  Google Scholar 

  3. Negami, S.: Classification of 6-regular Klein-bottlal graphs. Res. Rep. Inf. Sci. T.I.T. A-96 (1984)

  4. Negami, S.: Uniqueness and faithfulness of embedding of graphs into surfaces. Doctor thesis, Tokyo Institute of Technology, 1985

  5. Plummer M.D.: A theorem on matchings in the plane, Graph Theory in Memory of G. A. Dirac. Ann. Discrete. Math. 41, 347–354 (1989)

    Article  MathSciNet  Google Scholar 

  6. Plummer M.D.: Extending matchings in planar graphs IV. Discrete Math. 109, 207–219 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Plummer M.D.: Matching extension and the genus of graph. J. Combin. Theory. Ser. B. 44, 329–337 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Aldred R.R.L., Plummer M.D.: Restricted matching in graphs of small genus. Discrete Math. 308, 5907–5921 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Thomas R., Yu X.: 4-Connected projective planar graphs are Hamiltonian. J. Combin. Theory Ser. B. 62, 114–132 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Thomas R., Yu X.: Five-connected toroidal graphs are Hamiltonian. J. Combin. Theory Ser. B. 69, 79–96 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Thomassen R.: A theorem on paths in planar graphs. J. Lond. Math. Soc. 22, 169–176 (1983)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Department of Information Media and Environment Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan

    Iwao Mizukai

  2. Faculty of Education and Human Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan

    Seiya Negami

  3. Tsuruoka National College of Technology, Tsuruoka, Yamagata, 997-8511, Japan

    Yusuke Suzuki

Authors
  1. Iwao Mizukai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seiya Negami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yusuke Suzuki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seiya Negami.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mizukai, I., Negami, S. & Suzuki, Y. The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle. Graphs and Combinatorics 26, 549–557 (2010). https://doi.org/10.1007/s00373-010-0927-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-010-0927-8

Keywords

Search

Navigation