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The complexity of completing partial Latin squares

✍ Scribed by Charles J. Colbourn


Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
400 KB
Volume
8
Category
Article
ISSN
0166-218X

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We show that any partial 3r Γ—3r Latin square whose filled cells lie in two disjoint r Γ—r sub-squares can be completed. We do this by proving the more general result that any partial 3r by 3r Latin square, with filled cells in the top left 2r Γ— 2r square, for which there is a pairing of the columns s

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This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t;j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2; : : : ; 7 and odd n 6 21, and

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