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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



The Dinitz problem solved for rectangles

Author: Jeannette C. M. Janssen
Journal: Bull. Amer. Math. Soc. 29 (1993), 243-249
MSC (2000): Primary 05B15; Secondary 05C15
MathSciNet review: 1215310
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Abstract: The Dinitz conjecture states that, for each n and for every collection of n-element sets $ {S_{ij}}$, an $ n \times n$ partial latin square can be found with the $ (i,j){\text{th}}$ entry taken from $ {S_{ij}}$. The analogous statement for $ (n - 1) \times n$ rectangles is proven here. The proof uses a recent result by Alon and Tarsi and is given in terms of even and odd orientations of graphs.

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Article copyright: © Copyright 1993 American Mathematical Society

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