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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13402 |
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| _version_ | 1866913398152757248 |
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| author | Hendrey, Kevin Illingworth, Freddie Kamčev, Nina Tan, Jane |
| author_facet | Hendrey, Kevin Illingworth, Freddie Kamčev, Nina Tan, Jane |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When $t$-intersecting hypergraphs admit bounded $c$-strong colourings Hendrey, Kevin Illingworth, Freddie Kamčev, Nina Tan, Jane Combinatorics 05C15 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. |
| title | When $t$-intersecting hypergraphs admit bounded $c$-strong colourings |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2406.13402 |