On rainbow-free colourings of uniform hypergraphs

Ragnar Groot Koerkamp; Stanislav Živný

doi:10.1016/j.tcs.2021.06.022

On rainbow-free colourings of uniform hypergraphs

Combinatorics 2021-08-30 v1 Discrete Mathematics

Authors: Ragnar Groot Koerkamp , Stanislav Živný

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Abstract

We study rainbow-free colourings of $k$ -uniform hypergraphs; that is, colourings that use $k$ colours but with the property that no hyperedge attains all colours. We show that $p^*=(k-1)(\ln n)/n$ is the threshold function for the existence of a rainbow-free colouring in a random $k$ -uniform hypergraph.

Keywords

rainbow-free colourings k-uniform hypergraphs random hypergraphs threshold function extremal combinatorics

Cite

@article{arxiv.2106.07072,
  title  = {On rainbow-free colourings of uniform hypergraphs},
  author = {Ragnar Groot Koerkamp and Stanislav Živný},
  journal= {arXiv preprint arXiv:2106.07072},
  year   = {2021}
}

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