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Abstract
A. Vince introduced a natural generalization of graph coloring and proved same basic facts, revealing it to be a concept of interest. The coloring theory for digraphs is similar to the coloring theory for undirected graphs when independent sets of vertices are replaced by acyclic sets. Since the directed K-cycle has circular chromatic umber for values of between and are possible. In fact, takes on all rational values greater than . Now if and only if a particular digraph is acyclic and the decision problem associated with this question is probably not in NP through it is both NP hard and NP easy.
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References
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