The proper language to use here is to speak
of coloring a graph in such a way that each of
the nine colors appears in every row, column, and
box of the puzzle. Such a coloring is a solution
of the puzzle and is known in graph theory as a
proper coloring. The minimum number of colors
required for a proper coloring of G is called the
chromatic number of G, and for Sudoku graphs
the chromatic number is, of course