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arXiv · 2607.18667

Strong Colouring of the Qualitative Independence Hypergraph $3\text{-}QI(11,2)$

Raina Mary Thomas·Yasmeen Akhtar
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Abstract

We determine the strong independence number of the qualitative independence hypergraph, $3\text{-}QI(11, 2)$, using a technique that involves considering its vertices as subsets of $\{1,2, \ldots, 11\}$ and assessing them as intersecting set systems. This gives the maximum size of colour classes in any strong colouring and thus, a lower bound on the strong chromatic number of $3\text{-}QI(11,2)$. We leverage this bound along with an upper bound of the strong chromatic number of $3\text{-}QI(10,2)$, to consequently, establish that the covering array number of $3\text{-}QI(11, 2)$, $CAN(3\text{-}QI(11,2),2) = 11$ and give a sufficient condition for a hypergraph $H$ to have $CAN(H, 2)=11$.

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Raina Mary Thomas, Yasmeen Akhtar. 2026-07-21. Strong Colouring of the Qualitative Independence Hypergraph $3\text{-}QI(11,2)$. https://arxiv.org/abs/2607.18667

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