  An Euler tour in a hypergraph is a closed walk that traverses each edge of
the hypergraph exactly once, while an Euler family is a family of closed walks
that jointly traverse each edge exactly once and cannot be concatenated. In
this paper, we show how the problem of existence of an Euler tour (family) in a
hypergraph $H$ can be reduced to the analogous problem in some smaller
hypergraphs that are derived from $H$ using an edge cut of $H$. In the process,
new techniques of edge cut assignments and collapsed hypergraphs are
introduced. Moreover, we describe algorithms based on these characterizations
that determine whether or not a hypergraph admits an Euler tour (family), and
can also construct an Euler tour (family) if it exists.
