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arXiv · 2008.03827

Chain method for panchromatic colorings of hypergraphs

Margarita Akhmejanova·József Balogh
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Abstract

We deal with an extremal problem concerning panchromatic colorings of hypergraphs. A vertex $r$-coloring of a hypergraph $H$ is \emph{panchromatic} if every edge meets every color. We prove that for every $3<r\leq\sqrt[3]{n/(100\ln n)}$, every $n$-uniform hypergraph $H$ with $|E(H)|\leq \frac{1}{20r^2}\left(\frac{n}{\ln n}\right)^{\frac {r-1}{r}}\left(\frac{r}{r-1}\right)^{n-1}$ has a panchromatic coloring with $r$ colors.

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Margarita Akhmejanova, József Balogh. 2021-09-23. Chain method for panchromatic colorings of hypergraphs. https://arxiv.org/abs/2008.03827

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