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Coloring random graphs

  • Martin Fürer
  • C. R. Subramanian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 621)

Abstract

We present an algorithm for coloring random 3-chromatic graphs with edge probabilities below the n−1/2 “barrier”. Our (deterministic) algorithm succeeds with high probability to 3-color a random 3-chromatic graph produced by partitioning the vertex set into three almost equal sets and selecting an edge between two vertices of different sets with probability pn 3/5+ε. The method is extended to k-chromatic graphs, succeeding with high probability for pn−α+ε with α=2k/((k−l)(k+2)) and ε>0. The algorithms work also for Blum's balanced semi-random GSB(n,p,k) model where an adversary chooses the edge probability up to a small additive noise p. In particular, our algorithm does not rely on any uniformity in the degree.

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References

  1. 1.
    A. Blum, Some Tools for Approximate 3-Coloring, FOCS (1990), 554–562.Google Scholar
  2. 2.
    M.E. Dyer and A.M. Frieze, The Solution of Some Random NP-Hard Problems in Polynomial Expected Time, J. Alg. 10 (1989), 451–489.Google Scholar
  3. 3.
    M. Santha and U.V. Vazirani, Generating Quasi-random Sequences from Semi-random Sources, J. Comp. Syst. Sci. 33 (1986), 75–87.Google Scholar
  4. 4.
    J.S. Turner, Almost All k-colorable Graphs are Easy to Color, J. Alg. 9 (1988), 63–82.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Martin Fürer
    • 1
  • C. R. Subramanian
    • 1
  1. 1.Department of Computer SciencePennsylvania State UniversityUniversity ParkUSA

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