A note on completing latin squares

Lars-Daniel Öhman
2009 The Australasian Journal of Combinatorics  
We give a condition on the spatial distribution of filled cells in a partial Latin square P that is sufficient to ensure completability, regardless of what symbols are used in the filled cells. For example, if P is of the order mr + t, where m, r are positive integers and t ≥ 0, m is odd, and the filled cells of P are contained in the first m+1 2 r × r subsquares along the main diagonal, our condition is fulfilled, and P is completable. Another example is if P (of the same order) has non-empty
more » ... ells only in the m − 1 first r × r squares along the main diagonal and r ≥ m − 2. In this case, too, our condition holds, and P is completable.
dblp:journals/ajc/Ohman09 fatcat:k4fosd4ltreqln347hixa463h4