Strong Colouring of the Qualitative Independence Hypergraph 3-QI(11,2)

2026/07/21 by Raina Mary Thomas, Yasmeen Akhtar
Mathematics · #math.CO

paper · pdf

Abstract

We determine the strong independence number of the qualitative independence hypergraph, 3-QI(11, 2), using a technique that involves considering its vertices as subsets of \1,2, …, 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-QI(11,2). We leverage this bound along with an upper bound of the strong chromatic number of 3-QI(10,2), to consequently, establish that the covering array number of 3-QI(11, 2), CAN(3-QI(11,2),2) = 11 and give a sufficient condition for a hypergraph H to have CAN(H, 2)=11.

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