Webbläsaren som du använder stöds inte av denna webbplats. Alla versioner av Internet Explorer stöds inte längre, av oss eller Microsoft (läs mer här: * https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Var god och använd en modern webbläsare för att ta del av denna webbplats, som t.ex. nyaste versioner av Edge, Chrome, Firefox eller Safari osv.

Subgraph counts in random graphs using incomplete U-statistics methods

In English

Författare

Summary, in English

The random graph Kn,p is constructed on n labelled vertices by inserting each of the (n2) possible edges independently with probability p, 0> p < 1. For a fixed graph G, the threshold function for existence of a subgraph of Kn,p isomorphic to G has been determined by Erdös and Rényi [8] and Bollobás [3]. Bollobás [3] and Karo ski [14] have established asymptotic Poisson and normal convergence for the number of subgraphs of Kn,p isomorphic to G for sequences of p(n)→0 which are slightly greater than the threshold function. We use techniques from asymptotic theory in statistics, designed to study sums of dependent random variables known as U-statistics. We note that a subgraph count has the form of an incomplete U-statistics, and prove asymptotic normality of subgraph counts for a wide range of values of p, including any constant p and sequences of p(n) tending to 0 or 1 sufficiently slowly.

Publiceringsår

1988

Språk

Engelska

Sidor

299-310

Publikation/Tidskrift/Serie

Discrete Mathematics

Volym

72

Dokumenttyp

Artikel i tidskrift

Förlag

Elsevier

Ämne

  • Probability Theory and Statistics

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0012-365X