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Graphs and Combinatorics

, Volume 35, Issue 1, pp 353–361 | Cite as

Lower Bounds on the Uniquely Restricted Matching Number

  • M. Fürst
  • D. RautenbachEmail author
Original Paper
  • 22 Downloads

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.

Keywords

Matching Uniquely restricted matching Acyclic matching 

Notes

References

  1. 1.
    Baste, J., Rautenbach, D.: Degenerate matchings and edge colorings. Discret. Appl. Math. 239, 38–44 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baste, J., Rautenbach, D., Sau, I.: Uniquely restricted matchings and edge colorings. Lect. Notes Comput. Sci. 10520, 100–112 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Costa, V., Dantas, S., Rautenbach, D.: Matchings in graphs of odd regularity and girth. Discret. Math. 313, 2895–2902 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Flaxman, A.D., Hoory, S.: Maximum matchings in regular graphs of high girth. Electron. J. Comb. 14 (2007) (#N1) Google Scholar
  6. 6.
    Fürst, M., Rautenbach, D.: A lower bound on the acyclic matching number of subcubic graphs. Discret. Math. 341, 2353–2358 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Goddard, W., Hedetniemi, S.M., Hedetniemi, S.T., Laskar, R.: Generalized subgraph-restricted matchings in graphs. Discret. Math. 293, 129–138 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Golumbic, M.C., Hirst, T., Lewenstein, M.: Uniquely restricted matchings. Algorithmica 31, 139–154 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Henning, M.A., Rautenbach, D.: Induced matchings in subcubic graphs without short cycles. Discret. Math. 315, 165–172 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Joos, F.: Induced matchings in graphs of bounded maximum degree. SIAM J. Discret. Math. 30, 1876–1882 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Joos, F., Rautenbach, D., Sasse, T.: Induced matchings in subcubic graphs. SIAM J. Discret. Math. 28, 468–473 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lovász, L., Plummer, M.D.: Matching Theory. Annals of Discrete Mathematics, vol. 29. North-Holland, Amsterdam (1986)zbMATHGoogle Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Optimization and Operations ResearchUlm UniversityUlmGermany

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