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We prove that the maximum number of edges in a k-uniform hypergraph on n vertices containing no 2-regular subhypergraph is (n−1k−1) if k⩾4 is even and n is sufficiently large. Equality holds only if all edges contain a specific vertex v. For odd k we conjecture that this maximum is (n−1k−1)+⌊n−1k⌋, with equality only for the hypergraph described above plus a maximum matching omitting v.
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