## 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 zy are already in the graph and xzy∈ H. We say that the process propagates if it reaches the complete graph before it terminates. In this paper we prove that the threshold probability for propagation is p = 1/2√n. We conclude 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) | 1-19 |

Number of pages | 19 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 30 |

Issue number | 1 |

DOIs | |

State | Published - 2016 |

### Bibliographical note

Funding Information:Email: yuvalp@cs.huji.ac.il. Yuval Peled is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship. 3 Email: benjamin.sudakov@math.ethz.ch. Research supported in part by SNSF grant 200021-149111.

Publisher Copyright:

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

## Keywords

- Differential equation method
- Propagation
- Random simplicial complexes
- Triadic process