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Dominating Induced Matchings

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Graph Theory, Computational Intelligence and Thought

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5420))

Abstract

We study the problem of determining whether or not a graph G has an induced matching that dominates every edge of the graph, which is also known as efficient edge domination. This problem is known to be NP-complete in general as well as in some restricted domains, such as bipartite graphs or regular graphs. In this paper, we identify a graph parameter to which the complexity of the problem is sensible and produce results of both negative (intractable) and positive (solvable in polynomial time) type.

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References

  1. Brandstädt, A., Eschen, E.M., Sritharan, R.: The induced matching and chain subgraph cover problems for convex bipartite graphs. Theoret. Comput. Sci. 381, 260–265 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cameron, K.: Induced matchings. Discrete Appl. Math. 24, 97–102 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Courcelle, B., Makowsky, J.A., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput.  Syst. 33, 125–150 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cardoso, D.M., Cerdeira, J.O., Delorme, C., Silva, P.C.: Efficient edge domination in regular graphs. Discrete App. Math. 156, 3060–3065 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Golumbic, M.C., Rotics, U.: On the clique-width of some perfect graph classes. International J. Foundations of Computer Sci. 11, 423–443 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Golumbic, M.C., Lewenstein, M.: New results on induced matchings. Discrete Appl. Math. 101, 157–165 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Grinstead, D.L., Slater, P.J., Sherwani, N.A., Holmes, N.D.: Efficient edge domination problems in graphs. Inform. Process. Lett. 48, 221–228 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kobler, D., Rotics, U.: Finding maximum induced matchings in subclasses of claw-free and \(P\sb 5\)-free graphs, and in graphs with matching and induced matching of equal maximum size. Algorithmica 37, 327–346 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kratochvíl, J.: Regular codes in regular graphs are difficult. Discrete Math 133, 191–205 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lozin, V.V.: On maximum induced matchings in bipartite graphs. Inform. Process. Lett. 81, 7–11 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lozin, V.V., Rautenbach, R.: The tree- and clique-width of bipartite graphs in special classes. Australasian J. Combinatorics 34, 57–67 (2006)

    MathSciNet  MATH  Google Scholar 

  12. Lu, C.L., Ko, M.-T., Tang, C.Y.: Perfect edge domination and efficient edge domination in graphs. Discrete Appl. Math. 119, 227–250 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu, C.L., Tang, C.Y.: Solving the weighted efficient edge domination problem on bipartite permutation graphs. Discrete Appl. Math. 87, 203–211 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Makowsky, J.A., Rotics, U.: On the clique-width of graphs with few P 4’s. International J. Foundations of Computer Sci. 10, 329–348 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Matemática da Universidade de Aveiro, 3810-193, Aveiro, Portugal

    Domingos M. Cardoso

  2. DIMAP and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Vadim V. Lozin

Authors
  1. Domingos M. Cardoso
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  2. Vadim V. Lozin
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Editor information

Editors and Affiliations

  1. The Caesarea Rothschild Institute, Mount Carmel, University of Haifa, 31905, Haifa, Israel

    Marina Lipshteyn

  2. Department of Computer Science and Mathematics, Ariel University Center of Samaria, 40700, Ariel, Israel

    Vadim E. Levit

  3. Department of Computer Science, Colorado State University, 80523-1873, Fort Collins, CO, USA

    Ross M. McConnell

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© 2009 Springer-Verlag Berlin Heidelberg

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Cardoso, D.M., Lozin, V.V. (2009). Dominating Induced Matchings. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-02029-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02028-5

  • Online ISBN: 978-3-642-02029-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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