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Completing partial Latin squares with one filled row, column and symbol
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 313, no 9, 1011-1017 p.Article in journal (Refereed) Published
Abstract [en]

Let P be an n x n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbols. Assume further that s is the symbol of cell (r, c) in P. We prove that P is completable to a Latin square if n >= 8 and n is divisible by 4, or n <= 7 and n is not an element of {3, 4, 5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square. (C) 2013 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2013. Vol. 313, no 9, 1011-1017 p.
Keyword [en]
Latin square, Partial Latin square, Completing partial Latin squares
National Category
Discrete Mathematics
URN: urn:nbn:se:umu:diva-71068DOI: 10.1016/j.disc.2013.01.019ISI: 000317327200005OAI: diva2:630084
Available from: 2013-06-18 Created: 2013-05-20 Last updated: 2013-06-18Bibliographically approved

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Häggkvist, Roland
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