Component structure in the evolution of random hypergraphs

Abstract

The component structure of the most general random hypergraphs, with edges of differen sizes, is analyzed. We show that, as this is the case for random graphs, there is a “double jump” in the probable and almost sure size of the greatest component of hypergraphs, when the average vertex degree passes the value 1.

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Schmidt-Pruzan, J., Shamir, E. Component structure in the evolution of random hypergraphs. Combinatorica 5, 81–94 (1985). https://doi.org/10.1007/BF02579445

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AMS subject classification (1980)

  • 05 C 65
  • 60 C 05