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Computing a perfect matching in a line graph

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VLSI Algorithms and Architectures (AWOC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 319))

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Abstract

We show in this paper that a perfect matching of a line graph can be computed in NC. A necessary and sufficient condition for a line graph to have a perfect matching is an even number of vertices. To compute the perfect matching, we use a technique of dividing the graph into kingdoms. This result is equivalent to partitioning the edge set of a graph into edge disjoint paths of even length.

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References

  1. Marek Chrobak and Joseph Naor, “Perfect Matchings in Claw Free Graphs”, In preparation.

    Google Scholar 

  2. G. Chartrand, A. D. Polimeni and M. James Stewart, “The Existance of 1-Factors in Line Graphs, Squares and Total Graphs”, Indag. Math. 35, pp. 228–232 (1973).

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  3. D. Y. Grigoriev and M. Karpinski, “The Matching Problem for Bipartite Graphs with Polynomially Bounded Permanents is in NC”, 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles, CA, 1987.

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  4. M. Goldberg and T. Spencer, “A New Parallel Algorithm for the Maximal Independent Set Problem”, 28th Annual IEEE Symposium on Foundations of Computer Science, Los Angeles, CA, 1987.

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  5. R. M. Karp, E. Upfal and A. Wigderson, “Constructing a Perfect Matching is in Random NC”, Combinatorica, Vol. 6, 1, pp. 35–48, (1986).

    MATH  MathSciNet  Google Scholar 

  6. Mauricio Karchmer and Joseph Naor, “A Fast Parallel Algorithm for Coloring a Graph with Δ Colors”, Journal of Algorithms, Vol. 9, 1, pp. 83–91, (1988).

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Luby, “A simple parallel algorithm for the maximal independent set”, Siam Journal on Computing, Vol. 15, 4, (1986).

    Google Scholar 

  8. K. Mulmuley, U. V. Vazirani and V. V. Vazirani, “Matching is as easy as Matrix Inversion”, Combinatorica, Vol. 7, 1, pp. 105–113, (1987).

    MATH  MathSciNet  Google Scholar 

  9. J. Petersen, “Die Theorie der Regulären Graphs”, Acta Math. Vol. 15, pp. 193–220 (1891).

    Article  MATH  Google Scholar 

  10. D. P. Sumner, “On Tutte's Factorization Theorem”, Proceedings of the Capital Conference on Graph Theory and Combinatorics, George Washington University, Washington D.C., 1973, pp. 350–355. Lecture Notes in Math., Vol. 406, Springer, Berlin, 1974.

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Authors and Affiliations

  1. Department of Computer Science, University of Southern California, 90089-0782, Los Angeles, CA

    Joseph Naor

Authors
  1. Joseph Naor
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Editor information

John H. Reif

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© 1988 Springer-Verlag Berlin Heidelberg

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Naor, J. (1988). Computing a perfect matching in a line graph. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040382

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  • DOI: https://doi.org/10.1007/BFb0040382

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96818-6

  • Online ISBN: 978-0-387-34770-7

  • eBook Packages: Springer Book Archive

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