Random graph orders

نویسندگان

  • Michael H. Albert
  • Alan M. Frieze
چکیده

Let Pn be the order determined by taking a random graph G on {l,2,...,n}, directing the edges from the lesser vertex to the greater (as integers), and then taking the transitive closure of this relation. We call such an ordered set a random graph order. We show that there exist constants c, and a, such that the expected height and set up number of Pn are sharply concentrated around en and cm respectively. We obtain the estimates: .565<c<.610, and .034<a<.289. We also discuss the width, dimension, and first-order properties of Pn. AMS (MOS) subject classifications (1985). Primary: 06A10 Secondary: 05C80, 60C05.

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تاریخ انتشار 2015