  The information rate for an access structure is the reciprocal of the load of
the optimal secret sharing scheme for this structure. We determine this value
for all trees: it is 1/(2-1/c), where c is the size of the largest core of the
tree. A subset of the vertices of a tree is a core if it induces a connected
subgraph and for each vertex in the subset one finds a neighbor outside the
subset. Our result follows from a lower and an upper bound on the information
rate that applies for any graph and happen to coincide for trees because of a
correspondence between the size of the largest core and a quantity related to a
fractional cover of the tree with stars.
