ABSTRACT
A partial latin square of order n (PLS(n)) is an n×n array whose cells are either empty or contain an element of N such that each element occurs in at most one cell of each row or column. A PLS is maximal (MPLS) if no nonempty cell can be filled without violating this condition. This chapter provides introduction of the maximal partial latin squares. It presents appropriate results of the maximal partial latin squares along with theorem and proofs as well as lemmas. The chapter deals with determining the spectrum for maximal partial latin squares of order n. Two distinct cells of a PLS are said to be neighbors if they are in the same row or in the same column.
