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A graph G is r-equitably k-colorable if its vertex set can be partitioned into k independent sets, any two of which differ in size by at most r. The r-equitable chromatic threshold of a graph G, denoted by χ * r= (G), is the minimum k such that G is r-equitably k ′-colorable for all k ′ ≥ k. Let G × H denote the Kronecker product of graphs G and H. In this… (More)

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