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A total coloring of a simple graph G is a coloring of both the edges and the vertices. A total coloring is proper if no two adjacent or incident elements receive the same color. The minimum number of colors required for a proper total coloring of G is called the total chromatic number of G and denoted by χt(G). The Total Coloring Conjecture (TCC) states that for every simple graph G, Δ(G)+1≤χt(G)≤Δ(G)+2...
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