Related necessary conditions for completing partial latin squares |
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| Authors: | Rick Giles T Oyama LE Trotter |
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| Institution: | 1. Department of Mathematics, University of Kentucky, Lexington, Kentucky USA;2. Institute for Operations Research, Bonn University, Bonn, West Germany;3. School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New YorkUSA;4. Institute for Operations Research, Bonn University, Bonn, West Germany |
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| Abstract: | Three classes of necessary conditions for completing partial latin squares are studied. These condition classes are derived via network flow theory, bipartite graph matching theory and by relating the completion problem to triply stochastic matrices. The latter formulation suggest an integer programming model of the completion problem which is convenient for analyzing the relative strength of the three condition classes. It is shown that these classes are nested and examples are given to demonstrate that this nesting is proper. |
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