  We generalize the notion of orthogonal latin squares to colorings of simple
graphs. Two $n$-colorings of a graph are said to be \emph{orthogonal} if
whenever two vertices share a color in one coloring they have distinct colors
in the other coloring. We show that the usual bounds on the maximum size of a
certain set of orthogonal latin structures such as latin squares, row latin
squares, equi-$n$ squares, single diagonal latin squares, double diagonal latin
squares, or sudoku squares are a special cases of bounds on orthogonal
colorings of graphs.
