Maximal partial latin squares

Let ML(n) be the spectrum for maximal partial latin squares of order n, i.e. ML(n) = (t: there exists an MPLS(n) with exactly t non empty cells). This paper deals with determining the spectrum ML(n). The membership in ML(n) is decided for all n and t, 1 ;£ t ;£ n2, except for Horak and Rosa 2. Results Two distinct cells of a PLS are said to be neighbors if they are in the same row or in the same column. Thus each cell of a PLS(n) has 2n-1 …