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arXiv · 1808.05213

Quasi-transversal in Latin Squares

Adel P. Kazemi·Behnaz Pahlavsay
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Abstract

In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem involving Combinatorics is to find maximum number of disjoint transversals in a Latin square. So finding some family of decomposable Latin squares into disjoint transversals is our next aim. In the next section, we give an equivalent statement of a conjecture which has been attributed to Brualdi, Stein and Ryser by the concept of quasi-transversal. Finally, we prove the truth of the Rodney's conjecture for a family of graphs.

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Adel P. Kazemi, Behnaz Pahlavsay. 2018-08-15. Quasi-transversal in Latin Squares. https://arxiv.org/abs/1808.05213

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