On the completability of incomplete Latin squares

Authors:
Reinhardt Euler
Affiliations:
Faculté des Sciences, B.P.809, 20 Avenue Le Gorgeu, 29285 Brest Cedex, France
Venue:
European Journal of Combinatorics
Year:
2010

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Abstract

We introduce the notion of an availability matrix and apply a theorem of Frobenius-Konig to obtain necessary and sufficient conditions for the completability of an incomplete Latin row. We consider the related problem for two such rows within the framework of (1,2)-permutations and give solutions for several special cases. We also show how to extend these results to more than two rows. Finally, we present an integer programming formulation together with polyhedral results, and we discuss some consequences for class-teacher time-table problems.