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.
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“The secret of genius is to suffer no fiction to exist for us; to realize all that we know; in the high refinement of modern life, in arts, in sciences, in books, in men, to exact good faith, reality, and a purpose; and first, last, midst, and without end, to honor every truth by use.”
—Ralph Waldo Emerson (1803–1882)