Possible Duplicate:
Partial latin square with $\le n-1$ filled cells
http://ajc.maths.uq.edu.au/pdf/22/ocr-ajc-v22-p247.pdf
Could someone please further explain the inductive step here in Theorem 5 in more explicit terms, or write the proof in explicit terms? I'm afraid I don't see how the inductive step makes sense for the completion of a Latin square.