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Dimitris Achlioptas, Assaf Naor, The Two Possible Values of the Chromatic Number of a Random Graph, Annals of Mathematics, Second Series, Vol. 162, No. 3 (Nov., 2005), pp. 1335-1351 ...
Abstract The adjacent vertex-distinguishing total chromatic number of a graph 𝐺, denoted by χ𝑎𝑡 (𝐺), is the smallest denoted by 𝑘 for which 𝐺 has a proper total 𝑘-coloring such that any two ...