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Induced Matchings in Regular Graphs and Trees

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Graph-Theoretic Concepts in Computer Science (WG 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

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Abstract

This paper studies the complexity of the Maximum Induced Matching problem (MIM) in regular graphs and trees. We show that the largest induced matchings in a regular graph of degree d can be approximated with a performance ratio less than d. However MIM is NP-hard to approximate within some constant c > 1 even if the input is restricted to various classes of bounded degree and regular graphs. Finally we describe a simple algorithm providing a linear time optimal solution to MIM if the input graph is a tree.

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References

  1. N. Alon, U. Feige, A. Wigderson, and D. Zuckerman. Derandomized Graph Products. Computational Complexity, 5:60–75, 1995. 96

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Berman and M. Karpinski. On Some Tighter Inapproximability Results. In Proc. 26th I.C.A.L.P., Springer-Verlag, 1999. 96

    Google Scholar 

  3. K. Cameron. Induced Matchings. Discr. Applied Math., 24(1-3):97–102, 1989. 90,98

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Crescenzi. A Short Guide to Approximation Preserving Reductions. In Proc. 12th Conf. on Comput. Complexity, pages 262–273, Ulm, 1997. 93

    Google Scholar 

  5. P. Erd?os. Problems and Results in Combinatorial Analysis and Graph Theory. Discr. Math., 72:81–92, 1988. 89

    Article  Google Scholar 

  6. R. J. Faudree, A. Gyárfas, R. H. Schelp, and Z. Tuza. Induced Matchings in Bipartite Graphs. Discr. Math., 78(1-2):83–87, 1989. 89

    Article  MATH  Google Scholar 

  7. F. Gavril. Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques and Maximum Independent Set of a Chordal Graph. SIAM J. Comp., 1(2):180–187, June 1972. 90, 98

    Article  MATH  MathSciNet  Google Scholar 

  8. M. R. Garey and D. S. Johnson. Computer and Intractability, a Guide to the Theory of NP-Completeness. Freeman and Company, 1979. 94

    Google Scholar 

  9. B. Korte and D. Hausmann. An Analysis of the Greedy Heuristic for Independence Systems. Ann. Discr. Math., 2:65–74, 1978. 90

    Article  MATH  MathSciNet  Google Scholar 

  10. S. Khanna and S. Muthukrishnan. Personal communication. 94

    Google Scholar 

  11. J. Liu and H. Zhou. Maximum Induced Matchings in Graphs. Discr. Math., 170:277–281, 1997. 89

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994. 93

    Google Scholar 

  13. C. H. Papadimitriou and M. Yannakakis. Optimization, Approximation and Complexity Classes. J. Comp. Sys. Sciences, 43:425–440, 1991. 93

    Article  MATH  MathSciNet  Google Scholar 

  14. L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of Some Generalizations of the Maximum Matching Problem. I.P.L., 15(1):14–19, August 1982. 89

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Steger and M. Yu. On Induced Matchings. Discr. Math., 120:291–295, 1993. 89

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, L69 7ZF, UK

    Michele Zito

Authors
  1. Michele Zito
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Zito, M. (1999). Induced Matchings in Regular Graphs and Trees. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_10

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  • DOI: https://doi.org/10.1007/3-540-46784-X_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

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