  A trivalent diagram is a connected, two-colored bipartite graph (parallel
edges allowed but not loops) such that every black vertex is of degree 1 or 3
and every white vertex is of degree 1 or 2, with a cyclic order imposed on
every set of edges incident to to a same vertex. A rooted trivalent diagram is
a trivalent diagram with a distinguished edge, its root. We shall describe and
analyze an algorithm giving an exhaustive list of rooted trivalent diagrams of
a given size (number of edges), the list being non-redundant in that no two
diagrams of the list are isomorphic. The algorithm will be shown to have
optimal performance in that the time necessary to generate a diagram will be
seen to be bounded in the amortized sense, the bound being independent of the
size of the diagrams. That's what we call the CAT property. One objective of
the paper is to provide a reusable theoretical framework for algorithms
generating exhaustive lists of complex combinatorial structures with attention
paid to the case of unlabeled structures and to those generators having the CAT
property.
