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Subgraph counts in ...
Subgraph counts in random graphs using incomplete U-statistics methods
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- Nowicki, Krzysztof (författare)
- Lund University,Lunds universitet,Statistiska institutionen,Ekonomihögskolan,Department of Statistics,Lund University School of Economics and Management, LUSEM
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Wierman, John (författare)
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(creator_code:org_t)
- 1988
- 1988
- Engelska.
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Ingår i: Discrete Mathematics. - 0012-365X. ; 72, s. 299-310
- Relaterad länk:
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https://lup.lub.lu.s...
Abstract
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
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