  Detecting specific structures in a network has been a very active theme of
research in distributed computing for at least a decade. In this paper, we
start the study of subgraph detection from the perspective of local
certification. Remember that a local certification is a distributed mechanism
enabling the nodes of a network to check the correctness of the current
configuration, thanks to small pieces of information called certificates. Our
main question is: For a given graph $H$, what is the minimum certificate size
that allows checking that the network does not contain $H$ as a (possibly
induced) subgraph?
  We show a variety of lower and upper bounds, uncovering an interesting
interplay between the optimal certificate size, the size of the forbidden
subgraph, and the locality of the verification. Along the way we introduce
several new technical tools, in particular what we call the \emph{layered map},
which is not specific to forbidden subgraphs and that we expect to be useful
for certifying many other properties.
