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