## Abstract

Let F be a strictly k-balanced k-uniform hypergraph with e(F) ≥ |F|- k+ 1 and maximum co-degree at least two. The random greedy F-free process constructs a maximal F-free hypergraph as follows. Consider a random ordering of the hyper-edges of the complete k-uniform hypergraph K^{k}
_{n} on n vertices. Start with the empty hypergraph on n vertices. Successively consider the hyperedges e of K^{k}
_{n} in the given ordering and add e to the existing hypergraph provided that e does not create a copy of F. We show that asymptotically almost surely this process terminates at a hypergraph with Õ(nk-(|F|-k)/(e(F)-1)) hyperedges. This is best possible up to logarithmic factors.

Original language | English |
---|---|

Pages (from-to) | 73-77 |

Number of pages | 5 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 49 |

Early online date | 12 Nov 2015 |

DOIs | |

Publication status | Published - Nov 2015 |

## Keywords

- F-free process
- Hypergraph
- Random greedy

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics