### Abstract

A d-process for s-uniform hypergraphs starts with an empty hypergraph on n vertices, and adds one s-tuple at each time step, chosen uniformly at random from those 5-tuples which are not already present as a hyperedge and which consist entirely of vertices with degree less than d. We prove that for d ≥ 2 and s ≥ 3, with probability which tends to 1 as n tends to infinity, the final hypergraph is saturated; that is, it has n - i vertices of degree d and i vertices of degree d -1, where i = dn - ⌊sdn/s⌋. This generalises the result for s = 2 obtained by the second and third authors. In addition, when s ≥ 3, we prove asymptotic equivalence of this process and the more relaxed process, in which the chosen s-tuple may already be a hyperedge (and which therefore may form multiple hyperedges).

Original language | English |
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Pages (from-to) | 319-332 |

Number of pages | 14 |

Journal | Graphs and Combinatorics |

Volume | 20 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

## Cite this

*Graphs and Combinatorics*,

*20*(3), 319-332. https://doi.org/10.1007/s00373-004-0571-2