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      When \(t\)-intersecting hypergraphs admit bounded \(c\)-strong colourings

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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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          Author and article information

          Journal
          19 June 2024
          Article
          2406.13402
          13426f93-93ac-4dc9-9cd0-24b67aba63bb

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          05C15
          13 pages
          math.CO

          Combinatorics
          Combinatorics

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