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arXiv · 2106.07072

On rainbow-free colourings of uniform hypergraphs

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.

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Ragnar Groot Koerkamp, Stanislav Živný. 2021-06-13. On rainbow-free colourings of uniform hypergraphs. https://doi.org/10.1016/j.tcs.2021.06.022

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