On the diameters of spanning trees

The tree-diameter set of a connected graph
G
is the set of all diameters of the spanning trees of
G
, written in the increasing order. A relation between the consecutive elements of this set is obtained and it is shown to be the best possible. A sufficient condition for a set to be a feasible tree-diameter set is given and this solves a conjecture by Harary et al. on feasible tree-diameter sets.