## Abstract

Given a random 3-uniform hypergraph H=H(n, p) on n vertices where each triple independently appears with probability p, consider the following graph process. We start with the star G_{0} on the same vertex set, containing all the edges incident to some vertex v_{0}, and repeatedly add an edge xy if there is a vertex z such that xz and yz are already in the graph and xyz∈H. We say that the process propagates if all the edges are added to the graph eventually. In this paper we prove that the threshold probability for propagation is p=1/2√n. We also show that p=1/2√n is an upper bound for the threshold probability that a random 2-dimensional simplicial complex is simply-connected.

Original language | American English |
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Pages (from-to) | 189-196 |

Number of pages | 8 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 49 |

DOIs | |

State | Published - Nov 2015 |

### Bibliographical note

Publisher Copyright:© 2015 Elsevier B.V.

## Keywords

- Differential equation method
- Random simplicial complexes
- Triadic process