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A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to each other color class. The b-chromatic number of G is the maximum integer $$\chi _b(G)$$ χ b ( G ) for which G has a b-coloring with $$\chi _b(G)$$ χ b ( G ) colors. A graph G is b-continuous if G has a b-coloring with k colors, for every integer...
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