Date Added: Feb 2012
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 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. A vertex coloring of graph G=(V,E) is an assignment of colors to the vertices such that two adjacent vertices are assigned different colors.