An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings

Abstract

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.