Uniform forcing and immune sets in graphs and hypergraphs

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 networks and study minimum rank problems matrices graphs. This paper deals with zero hypergraphs. (Representing network by hypergraph allows us to account for its community structure more general interactions between subsets nodes.) We consider two natural generalizations hypergraphs graphs (one them already known) and, each one these we look into clutters play significant role process: clutter minimal sets immune sets. A formulation terms neighbourhoods (hence without making reference process) presented, highlighting behaviour distinct rules. Moreover, obtain families case complete provide full characterization uniform clutters, both case.