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On Universal Representation of Random Graphs
Andrzej Korzeniowski
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
korzeniowski@uta.edu
Annals of Combinatorics 7 (3) p.299-313 September, 2003
AMS Subject Classification: 05C80, 05C62
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, v2, ...} such that . In particular, for Bernoulli graphs with stable property Q, can be strengthened to: probability space set of infinite graphs with property Q such that and .
Keywords: Bernoulli graphs, infinite random graphs, representations

References:

1. B. Bollóbas, Random Graphs, Second Edition, Cambridge University Press, 2001.

2. J. Doob, Measure Theory, Springer-Verlag, 1994.

3. A. Korzeniowski, On Euler's Königsberg bridge problem for random graphs, J. Propag. Probab. Statist. 2 (1) (2001) 11ĘC18.

4. K. Stromberg, Probability for Analysts, Chapman & Hill, 1994.