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Published online by Cambridge University Press: 22 January 2025
For each uniformity $k \geq 3$, we construct
$k$ uniform linear hypergraphs
$G$ with arbitrarily large maximum degree
$\Delta$ whose independence polynomial
$Z_G$ has a zero
$\lambda$ with
$\left \vert \lambda \right \vert = O\left (\frac {\log \Delta }{\Delta }\right )$. This disproves a recent conjecture of Galvin, McKinley, Perkins, Sarantis, and Tetali.