Skip to main content
SpringerLink
Log in

Lower Bounds on the Uniquely Restricted Matching Number

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

Abstract

A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.

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

Fig. 1

Similar content being viewed by others

References

  1. Baste, J., Rautenbach, D.: Degenerate matchings and edge colorings. Discret. Appl. Math. 239, 38–44 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baste, J., Rautenbach, D., Sau, I.: Uniquely restricted matchings and edge colorings. Lect. Notes Comput. Sci. 10520, 100–112 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Biedl, T., Demaine, E.D., Duncan, C.A., Fleischer, R., Kobourov, S.G.: Tight bounds on maximal and maximum matchings. Discret. Math. 285, 7–15 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Costa, V., Dantas, S., Rautenbach, D.: Matchings in graphs of odd regularity and girth. Discret. Math. 313, 2895–2902 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Flaxman, A.D., Hoory, S.: Maximum matchings in regular graphs of high girth. Electron. J. Comb. 14 (2007) (#N1)

  6. Fürst, M., Rautenbach, D.: A lower bound on the acyclic matching number of subcubic graphs. Discret. Math. 341, 2353–2358 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goddard, W., Hedetniemi, S.M., Hedetniemi, S.T., Laskar, R.: Generalized subgraph-restricted matchings in graphs. Discret. Math. 293, 129–138 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Golumbic, M.C., Hirst, T., Lewenstein, M.: Uniquely restricted matchings. Algorithmica 31, 139–154 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Henning, M.A., Rautenbach, D.: Induced matchings in subcubic graphs without short cycles. Discret. Math. 315, 165–172 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Henning, M.A., Yeo, A.: Tight lower bounds on the size of a maximum matching in a regular graph. Graphs Comb. 23, 647–657 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Henning, M.A., Yeo, A.: Tight lower bounds on the matching number in a graph with given maximum degree. J. Graph Theory. 89(2), 115–149 (2018). https://doi.org/10.1002/jgt.22244

    Article  MathSciNet  MATH  Google Scholar 

  12. Joos, F.: Induced matchings in graphs of bounded maximum degree. SIAM J. Discret. Math. 30, 1876–1882 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Joos, F., Rautenbach, D., Sasse, T.: Induced matchings in subcubic graphs. SIAM J. Discret. Math. 28, 468–473 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lovász, L., Plummer, M.D.: Matching Theory. Annals of Discrete Mathematics, vol. 29. North-Holland, Amsterdam (1986)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Optimization and Operations Research, Ulm University, Ulm, Germany

    M. Fürst & D. Rautenbach

Authors
  1. M. Fürst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Rautenbach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Rautenbach.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fürst, M., Rautenbach, D. Lower Bounds on the Uniquely Restricted Matching Number. Graphs and Combinatorics 35, 353–361 (2019). https://doi.org/10.1007/s00373-018-1991-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-018-1991-8

Keywords

Search

Navigation