Toughness measures how well a graph remains connected after vertex deletions. Fan et al. (2023) presented spectral conditions for a graph to be t -tough. Motivated by their work, this paper investigates the adjacency spectrum of hypergraphs and establishes spectral radius conditions for t -tough in hypergraphs. These results extend the corresponding theories in graphs and provide a complete characterization of the extremal hypergraphs.
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Niu et al. (2026) studied this question.
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