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On factors in random graphs

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Abstract

The following result is proved: LetG n,p be a random graph withn vertices and probabilityp for an edge. Ifp is such that the random graph has min-degree at leastr with probability 1, then anyf-factor 1≦f≦r exists with probability 1, asn→∞.

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References

  1. D. Angluin and L. Valiant,Fast probabilistic algorithm for Hamiltonian circuits and matchings, J. Comput. Syst. Sci.18 (1979), 155–193.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Erdös and A. Rényi,On the evolution of random graphs, Publ. Math. Inst. Hungar. Acad. Sci.5A (1960), 17–61.

    MathSciNet  MATH  Google Scholar 

  3. P. Erdös and A. Rényi,On the strength of connectedness of a random graph, Acta Math. Acad. Sci. Hungar.12 (1961), 261–267.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Erdös and A. Rényi,On the existence of a factor of degree one of a connected random graph, Acta Math. Acad. Sci. Hungar.17 (1966), 359–368.

    Article  MathSciNet  MATH  Google Scholar 

  5. E.L. Lawler,Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, 1976.

  6. L. Pósa,Hamiltonian circuits in random graphs, Discrete Math.14 (1976), 359–364.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Shamir and E. Upfal,One factor in random graphs based on vertex choice, submitted, 1980.

  8. W. T. Tutte,The subgraph problem, Ann. Discrete Math.3 (1978), 289–295.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    E. Shamir & E. Upfal

  2. Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    E. Shamir & E. Upfal

Authors
  1. E. Shamir
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  2. E. Upfal
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Shamir, E., Upfal, E. On factors in random graphs. Israel J. Math. 39, 296–302 (1981). https://doi.org/10.1007/BF02761675

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  • DOI: https://doi.org/10.1007/BF02761675

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