  An optimal algorithm is presented about Conflict-Free Coloring for connected
subgraphs of tree of rings. Suppose the number of the rings in the tree is |T|
and the maximum length of rings is |R|. A presented algorithm in [1] for a Tree
of rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|)
colors. The coloring earned by this algorithm has the unique-min property, that
is, the unique color is also minimum.
