  A classical result in extremal graph theory is Mantel's Theorem, which states
that every maximum triangle-free subgraph of $K_n$ is bipartite. A sparse
version of Mantel's Theorem is that, for sufficiently large $p$, every maximum
triangle-free subgraph of $G(n,p)$ is w.h.p. bipartite. Recently, DeMarco and
Kahn proved this for $p > K \sqrt{\log n/n}$ for some constant $K$, and apart
from the value of the constant this bound is best possible. We study an
extremal problem of this type in random hypergraphs. Denote by $F_5$, which
sometimes called as the generalized triangle, the 3-uniform hypergraph with
vertex set {a,b,c,d,e} and edge set {abc, ade, bde}. One of the first extremal
results in extremal hypergraph theory is by Frankl and F\"{u}redi, who proved
that the maximum 3-uniform hypergraph on n vertices containing no copy of $F_5$
is tripartite for n>3000. A natural question is for what p is every maximum
$F_5$-free subhypergraph of $G^3(n,p)$ w.h.p. tripartite. We show this holds
for $p>K\log n/n$ for some constant K and does not hold for $p=0.1\sqrt{\log
n}/n$.
