  Zero forcing is an iterative coloring process on a graph that has been widely
used in such different areas as the modelling of propagation phenomena in
networks and the study of minimum rank problems in matrices and graphs. This
paper deals with zero forcing on hypergraphs. (Representing a network by a
hypergraph allows us to account for its community structure and for more
general interactions between different subsets of nodes.)
  We consider two natural generalizations to hypergraphs of zero forcing on
graphs (one of them already known) and, for each one of these generalizations
we look into two clutters that play a significant role in the forcing process:
the clutter of minimal forcing sets and the one of minimal immune sets. A
formulation of immune sets in terms of neighbourhoods (hence without making
reference to the iterative zero forcing process) is presented, highlighting the
different behaviour of the distinct forcing rules. Moreover, we obtain the
families of minimal forcing and minimal immune sets in the case of complete
hypergraphs and we provide a full characterization of forcing and immune
uniform clutters, both in the graph and in the hypergraph case.
