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The b-chromatic number of a graph $$G$$ G is a maximum integer $$\varphi (G)$$ φ ( G ) for which there exists a proper $$\varphi (G)$$ φ ( G ) -coloring with the additional property that each color class contains a vertex that is adjacent to one of the vertices within each color class. In contrast to many theoretical results discovered over the last decade and a half...
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