Critical sets for a pair of mutually orthogonal cyclic latin squares of odd order greater than 9

To date investigations on critical sets for a set of mutually orthogonal latin squares (MOLS) have been carried out only for small orders less than or equal to 9. In this paper we deal with a pair of cyclic orthogonal latin squares of order n, n greater than or equal to 11, n odd. Through construction of a uniquely completable set we give an upper bound on the size of the minimal critical set. In particular for n = 15 a critical set achieving this bound is obtained.