Component structure in the evolution of random hypergraphs
The authors generalize studies of Paul Erdős and A. Rényi on probable structure of random graphs with n labeled vertices and given density. They prove some theorems on the size \(C(d^*(n))\) of the greatest connected component in a random hypergraph. If the hypergraph has n vertices, the size of its largest edge is t, (2\(\leq t\leq 0(\ell n n))\) and the average vertex degree is \(d^*(n)\), then with probability tending to 1 when n tends to infinity: \(C(d^*(n))=0(t\quad \log n)\) for \(d<1\); \(C(d^*(n))=0(n^{2/3})\) for \(d\approx 1\); \(C(d^*(n))=0(n/t)\) for \(d>1\). It means here we can also find the well-known ''double jump'' which was described in case of random graphs.
scientific article; zbMATH DE number 3914363