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On the intricacy of avoiding multiple-entry arrays
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, no 20, 3030-3036 p.Article in journal (Refereed) Published
Abstract [en]

Let A be any n x n array on the symbols vertical bar n vertical bar = {1, . . . , n}, with at most in symbols in each cell. An n x n Latin square L on the symbols till is said to avoid A if no entry in L is present in the corresponding cell of A, and A is said to be avoidable if such a Latin square L exists. The intricacy of this problem is defined to be the minimum number of arrays into which A must be split in order to ensure that each part is avoidable. We present lower and upper bounds for the intricacy, and conjecture that the lower bound is in fact the correct answer. (C) 2012 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2012. Vol. 312, no 20, 3030-3036 p.
Keyword [en]
Latin square, Constraint satisfaction, List-coloring
National Category
URN: urn:nbn:se:umu:diva-60515DOI: 10.1016/j.disc.2012.07.003ISI: 000308450900007OAI: diva2:561575
Available from: 2012-10-19 Created: 2012-10-15 Last updated: 2012-10-19Bibliographically approved

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Öhman, Lars-Daniel
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