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arXiv · 2406.13402

When $t$-intersecting hypergraphs admit bounded $c$-strong colourings

Kevin Hendrey·Freddie Illingworth·Nina Kamčev·Jane Tan
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Abstract

The $c$-strong chromatic number of a hypergraph is the smallest number of colours needed to colour its vertices so that every edge sees at least $c$ colours or is rainbow. We show that every $t$-intersecting hypergraph has bounded $(t + 1)$-strong chromatic number, resolving a problem of Blais, Weinstein and Yoshida. In fact, we characterise when a $t$-intersecting hypergraph has large $c$-strong chromatic number for $c\geq t+2$. Our characterisation also applies to hypergraphs which exclude sunflowers with specified parameters.

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Kevin Hendrey, Freddie Illingworth, Nina Kamčev, Jane Tan. 2024-06-19. When $t$-intersecting hypergraphs admit bounded $c$-strong colourings. https://arxiv.org/abs/2406.13402

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