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When are random graphs connected

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Abstract

Several results concerning the connectivity of infinite random graphs are considered. A necessary sufficient condition for a zero–one law to hold is given when the edges are chosen independently. Some specific examples are treated including one where the vertex set isN and the probability that an edge joiningi toj is present depends only on |i−j|.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    S. Kalikow & B. Weiss

Authors
  1. S. Kalikow
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  2. B. Weiss
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Kalikow, S., Weiss, B. When are random graphs connected. Israel J. Math. 62, 257–268 (1988). https://doi.org/10.1007/BF02783296

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  • DOI: https://doi.org/10.1007/BF02783296

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