  One model of message delivery in a computer network is based on labelling
each edge by a subset of a (reasonably small) universal set, and then encoding
a path as the union of the labels of its edges. Earlier work suggested using
random edge labels, and that approach has a disadvantage of producing errors
(false positives). We demonstrate that if we make an assumption about the shape
of the network (in this paper we consider networks with a dense core and a
tree-like periphery) and assume that messages are delivered along shortest
paths, we can label edges in a way which prevents any false positives.
