On a generalization of the Evans Conjecture

The Evans Conjecture states that a partial Latin square of order n   with at most n-1n-1 entries can be completed. In this paper we generalize the Evans Conjecture by showing that a partial r-multi Latin square of order n   with at most n-1n-1 entries can be completed. Using this generalization, we confirm a case of a conjecture of Häggkvist.