For large n, any n-vertex r-uniform hypergraph with matching number < s has spectral radius at most that of F_{s-1}(n), with equality only for that hypergraph.
Frankl, Improved bounds for Erd˝ os’ matching conjecture,J
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A Spectral Confirmation of the Erd\H{o}s Matching Conjecture
For large n, any n-vertex r-uniform hypergraph with matching number < s has spectral radius at most that of F_{s-1}(n), with equality only for that hypergraph.