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Completing partial Latin squares with one filled row, column and symbol
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Department of Mathematics, Umeå University, Sweden.
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×n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbol s. 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∉{3,4,5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 313, no 9, 1011-1017 p.
Keyword [en]
Latin square, Partial Latin square, Completing partial Latin squares
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-92689DOI: 10.1016/j.disc.2013.01.019ISI: 000317327200005OAI: diva2:621678
Available from: 2013-05-16 Created: 2013-05-16 Last updated: 2013-05-24

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Casselgren, Carl Johan
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Mathematics and Applied MathematicsThe Institute of Technology
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