We propose a network protocol similar to the k-tree protocol of Itai and
Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we
define an {\em t-uncovering-by-bases} for a connected graph G to be a
collection U of spanning trees for G such that any t-subset of
edges of G is disjoint from at least one tree in U, where t is
some integer strictly less than the edge connectivity of G. We construct
examples of these for some infinite families of graphs. Many of these infinite
families utilise factorisations or decompositions of graphs. In every case the
size of the uncovering-by-bases is no larger than the number of edges in the
graph and we conjecture that this may be true in general.Comment: 12 pages, 5 figure