For large enough ground sets, every nontrivial t-intersecting k-uniform family has adjacency-tensor spectral radius bounded by the larger of two explicit extremal families, with equality only for copies of those families.
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A Spectral Hilton--Milner--Frankl Theorem for $t$-Intersecting Families
For large enough ground sets, every nontrivial t-intersecting k-uniform family has adjacency-tensor spectral radius bounded by the larger of two explicit extremal families, with equality only for copies of those families.