The order of the giant component of random hypergraphs

Authors:
Michael Behrisch;Amin Coja-Oghlan;Mihyun Kang
Affiliations:
Humboldt-Universität zu Berlin, Institut für Informatik, 10099 Berlin, Germany;University of Edinburgh, School of Informatics, Edinburgh EH8 9AB, UK;Technische Universität Berlin, Institut für Mathematik, 10623 Berlin, Germany
Venue:
Random Structures & Algorithms
Year:
2010

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Abstract

We establish central and local limit theorems for the number of vertices in the largest component of a random d-uniform hypergraph Hd(n,p) with edge probability p = c-$\left(\matrix{n-1 \cr d-1 }\right)$, where c (d - 1)-1 is a constant. The proof relies on a new, purely probabilistic approach. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010