Exact coloring
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In graph theory, an exact coloring is a (proper) vertex coloring in which every pair of colors appears on exactly one pair of adjacent vertices. In essence, an exact coloring is a coloring that is both harmonious and complete. Graphs that admit exact colorings have been classified.
External links
[1] (http://www.maths.dundee.ac.uk/~kedwards/biblio.html) A Bibliography of Harmonious Colourings and Achromatic Number by Keith Edwards