= Strong saturation of a uniform hypergraph
{title2=$e\notin E(H)\Longrightarrow\exists T\supseteq e:\ T^{(r)}\setminus\{e\}\subseteq E(H)$}
= Strongly saturated with respect to a complete uniform hypergraph
{synonym}
An $r$-<uniform hypergraph> is strongly saturated with respect to a complete uniform hypergraph of order $r+t$ when every missing edge immediately completes such a clique. Existing cliques are allowed. All $r$-sets meeting a fixed $t$-set give an example: the witness for a missing edge is its union with that fixed set. It has $\binom nr-\binom{n-t}{r}$ edges, and the <exterior-power quotient bound for strong hypergraph saturation> proves optimality.
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