Upper bounds on sets of orthogonal colorings of graphs

Abstract

We generalize the notion of orthogonal latin squares to colorings of simple graphs. Twon-colorings of a graph are said to be 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 special cases of bounds on orthogonal colorings of graphs.