## Abstract

We consider connected components in k-uniform hypergraphs for the following notion of connectedness: given integers k≥2 and 1≤j≤k−1, two j-sets (of vertices) lie in the same j-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least j vertices.

We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

Original language | English |
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Article number | P3.6 |

Number of pages | 17 |

Journal | The Electronic Journal of Combinatorics |

Volume | 26 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 |