  We say that a hypergraph $\mathcal{H}$ contains a graph $H$ as a trace if
there exists some set $S\subset V(\mathcal{H})$ such that
$\mathcal{H}|_S=\{h\cap S: h\in E(\mathcal{H})\}$ contains a subhypergraph
isomorphic to $H$. We study the largest number of hyperedges in uniform
hypergraphs avoiding some graph $F$ as trace. In particular, we determine this
number in the case $F=K_3$ and any uniformity, resolving a special case of a
conjecture of Mubayi and Zhao, and we improve a bound given by Luo and Spiro in
the case $F=C_4$ and uniformity 3.
