Advertisement

Maximum Induced Matchings in Grids

  • Ruxandra Marinescu-GhemeciEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 31)

Abstract

An induced matching in a graph is a matching such that no two edges are joined by an edge of G. For a connected graph G, denote by iμ(G) the maximum cardinality of an induced matching in G. In this paper we study the proble of finding a maximum induced matching in grid graphs with n lines and m columns—G n, m , and determine the exact value for iμ(G n, m ) when n or m are even.

Notes

Acknowledgements

I would like to thank Marc Demange from ESSEC Business School for suggesting me this problem and for his support.

References

  1. 1.
    Bonifaci, V., Korteweg, P., Marchetti-Spaccamela, A., and Stougie, L.: Minimizing flow time in the wireless gathering problem. ACM Transactions on Algorithms7(3), (2011) http://arxiv.org/abs/0802.2836.
  2. 2.
    Cameron, K.: Induced matchings. Discrete Appl. Math. 24, 97–102 (1989)zbMATHCrossRefGoogle Scholar
  3. 3.
    Cameron, K.: Induced matchings in intersection graphs. Discrete Math. 278, 1–9 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Cameron, K., Sritharan, R., Tang, Y.: Finding a maximum induced matching in weakly chordal graphs. Discrete Math. 266, 133–142 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dabrowski, K., Demange, M., and Lozin, V.V.: New results on maximum induced matchings in bipartite graphs and beyond. submitted, http://homepages.warwick.ac.uk/~mariaq/
  6. 6.
    Faudree, R.J., Gyárfas, A., Schelp, R.H., Tuza, Z.: Induced matchings in bipartite graphs. Discrete Math. 78, 83–87 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Golumbic, M.C., Lewenstein, M.: New results on induced matchings. Discrete Appl. Math. 101, 157–165 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kobler, D., Rotics, U.: Finding maximum induced matchings in subclasses of claw-free and P5-free graphs, and in graphs with matching and induced matching of equal maximum size. Algorithmica 37, 327–346 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Lozin, V.V.: On maximum induced matchings in bipartite graphs. Inform. Process. Lett. 81 7–11 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Rusu, I.: Maximum weight edge-constrained matchings. Discrete Appl. Math. 156, 662–672 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Stockmeyer, L.J., Vazirani, V.V.: Np-completeness of some generalizations of the maximum matching problem. I.P.L. 15, 14–19 (1982)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of BucharestBucharestRomania

Personalised recommendations