Subgraph counts in random graphs using incomplete U-statistics methods
Author
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.
Department/s
Publishing year
1988
Language
English
Pages
299-310
Publication/Series
Discrete Mathematics
Volume
72
Document type
Journal article
Publisher
Elsevier
Topic
- Probability Theory and Statistics
Status
Published
ISBN/ISSN/Other
- ISSN: 0012-365X