Displaying similar documents to “Completing partial Latin squares with two filled rows and two filled columns.”

When is an Incomplete 3 × n Latin Rectangle Completable?

Reinhardt Euler, Paweł Oleksik (2013)

Discussiones Mathematicae Graph Theory

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We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.

A class of latin squares derived from finite abelian groups

Anthony B. Evans (2014)

Commentationes Mathematicae Universitatis Carolinae

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We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.

Decomposing complete tripartite graphs into closed trails of arbitrary lengths

Elizabeth J. Billington, Nicholas J. Cavenagh (2007)

Czechoslovak Mathematical Journal

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The complete tripartite graph K n , n , n has 3 n 2 edges. For any collection of positive integers x 1 , x 2 , ⋯ , x m with ∑ i = 1 m x i = 3 n 2 and x i ≥ 3 for 1 ≤ i ≤ m , we exhibit an edge-disjoint decomposition of K n , n , n into closed trails (circuits) of lengths x 1 , x 2 , ⋯ , x m .