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  "body": "\n## Statement\n\nConsider an $h$-uniform hypergraph $H$ with $v(H)$ vertices. The supersaturation theorem states that for every $\\epsilon \u003e 0$, there exists a $\\delta \u003e 0$ such that if $G$ is an $h$-uniform hypergraph on $n$ vertices and at least $(\\pi(H) + \\epsilon) \\binom{n}{h}$ edges for $n$ sufficiently large, then there are at least $\\delta n^{v(H)}$ copies of $H$. \n\nEquivalently, we can restate this theorem as the following: If a graph $G$ with $n$ vertices has $o(n^{v(H)})$ copies of $H$, then there are at most $\\pi(H) \\binom{n}{2} + o(n^2)$ edges in $G$.\n",
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        "locator": "Forbidden subgraph problem, section Supersaturation \u003e Supersaturation Theorem",
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