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On Universal Representation of Random Graphs

Authors:	Email author" target="_blank">Andrzej?Korzeniowski Email author

Institution:	(1) Department of Mathematics, University of Texas at Arlington, 76019 Arlington, TX, USA

Abstract:	It is shown that every probability measure on the interval 0, 1] gives rise to a unique infinite random graph g on vertices {v₁, v₂, . . .} and a sequence of random graphs gn on vertices {v₁, . . . , v_n} such that $\mu (g_n \rightarrow g)$ . In particular, $\mathbf{P}(G-n(Q))$ for Bernoulli graphs with stable property Q, can be strengthened to: probability space (, F, P), set of infinite graphs G(Q) , F with property Q such that $P (G_n(Q) \rightarrow G(Q)) = 1 \quad \mathrm{and}\quad \mathbf{P}(G-n(Q)) = P(G_n(Q))$ .AMS Subject Classification: 05C80, 05C62.

Keywords:	Bernoulli graphs infinite random graphs representations
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