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A Sharp Threshold for a Non-monotone Digraph Property

  • Jean-Marie Le Bars
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We define a non-monotone digraph property TOUR1, a variant of the digraph property KERNEL, which refines the notion of maximal tournament. First we prove that there is a constant 0 < α < 1 such that TOUR1 is asymptotically almost surely true in random digraphs with constant arc probability p ≤ α and asymptotically almost surely false in random digraphs with constant arc probability p > α. Then we concentrate our study on random digraphs with arc probability close to a and we obtain a sharp threshold.

Keywords

Random Graph Monotone Property Moment Method Small Positive Constant Edge Probability 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Jean-Marie Le Bars
    • 1
  1. 1.Université de CaenCampus cote de nacreCAENFrance

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