ON THE CHROMATIC INDEX OF LATIN SQUARES

Abstract

A proper coloring of a Latin square of order n is an assignment of colors to its elements triples such that each row, column and symbol is assigned n distinct colors. Equivalently, a proper coloring of a Latin square is a partition into partial transversals. The chromatic index of a Latin square is the least number of colors needed for a proper coloring. We study the chromatic index of the cyclic Latin square which arises from the addition table for the integers modulo n . We obtain the best possible bounds except for the case when n/ 2 is odd and divisible by 3. We make some conjectures about the chromatic index, suggesting a generalization of Ryser’s conjecture (that every Latin square of odd order contains a transversal).