On small non-uniform hypergraphs without property B

Danila Cherkashin

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arXiv · 2303.03803

On small non-uniform hypergraphs without property B

Danila Cherkashin

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Abstract

For a given hypergraph $H = (V,E)$ consider the sum $q(H)$ of $2^{-|e|}$ over $e \in E$. Consider the class of hypergraphs with the smallest edge of size $n$ and without a 2-colouring without monochromatic edges. Let $q(n)$ be the smallest value of $q(H)$ in this class. We provide a survey of the known bounds on $q(n)$ and make some minor refinements.

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Danila Cherkashin. 2023-03-07. On small non-uniform hypergraphs without property B. https://arxiv.org/abs/2303.03803

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