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Packing Edges in Random Regular Graphs

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Mathematical Foundations of Computer Science 2002 (MFCS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense). We consider the problem of approximating the solution to the maximum k-separated matching problem in random r-regular graphs for each fixed integer k and each fixed r ≥ 3. We prove both constructive lower bounds and combinatorial upper bounds on the size of the optimal solutions.

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References

  1. J. Aronson, A. Frieze, and B. G. Pittel. Maximum matchings in sparse random graphs: Karp-sipser revisited. Random Structures and Algorithms, 12:111–178, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Cameron. Induced matchings. Discrete and Applied Mathematics, 24(1–3):97–102, 1989.

    MATH  MathSciNet  Google Scholar 

  3. J. R. Cash and A. H. Karp. A variable order runge-kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software, 16(3):201–222, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Duckworth, D. Manlove, and M. Zito. On the approximability of the maximum induced matching problem. Technical Report TR-2000-56, Department of Computing Science of Glasgow University, April 2000.

    Google Scholar 

  5. W. Duckworth, N. C. Wormald, and M. Zito. Maximum induced matchings of random cubic graphs. In D. Z. Du, P. Eades, V. Estivill-Castro, X. Lin, and A. Sharma, editors, Computing and Combinatorics; 6th Annual International Conference, COCOON’00, volume 1858 of Lecture Notes in Computer Science, pages 34–43. Springer-Verlag, 2000.

    Google Scholar 

  6. W. Duckworth, N. C. Wormald, and M. Zito. Maximum induced matchings of random cubic graphs. Journal of Computational and Applied Mathematics, 142(1):39–50, 2002. Preliminary version appeared in [5].

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Edmonds. Paths, trees and flowers. Canadian Journal of Mathematics, 15:449–467, 1965.

    MathSciNet  Google Scholar 

  8. P. Erdos. Problems and results in combinatorial analysis and graph theory. Discrete Mathematics, 72:81–92, 1988.

    Article  MathSciNet  Google Scholar 

  9. R. J. Faudree, A. Gyárfas, R. H. Schelp, and Z. Tuza. Induced matchings in bipartite graphs. Discrete Mathematics, 78(1–2):83–87, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. W. Gear. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, 1971.

    Google Scholar 

  11. S. Janson, T. OLuczak, and A. Rucínski. Random Graphs. John Wiley and Sons, 2000.

    Google Scholar 

  12. J. Liu and H. Zhou. Maximum induced matchings in graphs. Discrete Mathematics, 170:277–281, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  13. L. Lovász and M. D. Plummer. Matching Theory, volume 29 of Annals of Discrete Mathematics. North Holland, 1986.

    Google Scholar 

  14. R. Motwani. Average-case analysis of algorithms for matchings and related problems. Journal of the Association for Computing Machinery, 41(6):1329–1356, November 1994.

    Google Scholar 

  15. A. Steger and M. Yu. On induced matchings. Discrete Mathematics, 120:291–295, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  16. L. J. Stockmeyer and V. V. Vazirani. NP-Completeness of some generalizations of the maximum matching problem. Information Processing Letters, 15(1):14–19, August 1982.

    Google Scholar 

  17. N. C. Wormald. Differential equations for random processes and random graphs. Annals of Applied Probability, 5:1217–1235, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  18. N. C. Wormald. The differential equation method for random graph processes and greedy algorithms. In M. Karoński and H. J. Prömel, editors, Lectures on Approximation and Randomized Algorithms, pages 73–155. PWN, Warsaw, 1999.

    Google Scholar 

  19. M. Zito. Induced matchings in regular graphs and trees. In P. Widmayer, G. Neyer, and S. Eidenbenz, editors, Graph Theoretic Concepts in Computer Science; 25th International Workshop, WG’99, volume 1665 of Lecture Notes in Computer Science, pages 89–100. Springer-Verlag, 1999.

    Google Scholar 

  20. M. Zito. Randomised Techniques in Combinatorial Algorithmics. PhD thesis, Department of Computer Science, University of Warwick, 1999.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, Sydney, NSW, 2109, Australia

    William Duckworth

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

    Mihalis Beis & Michele Zito

Authors
  1. Mihalis Beis
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  2. William Duckworth
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  3. Michele Zito
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

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© 2002 Springer-Verlag Berlin Heidelberg

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Beis, M., Duckworth, W., Zito, M. (2002). Packing Edges in Random Regular Graphs. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_9

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  • DOI: https://doi.org/10.1007/3-540-45687-2_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

  • eBook Packages: Springer Book Archive

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