%0 Journal Article
%T Unavoidable arrays
%A Klas Markstr£¿m
%A Lars-Daniel £¿hman
%J Contributions to Discrete Mathematics
%D 2010
%I University of Calgary
%X An $n imes n$ array is emph{avoidable} if for each set of $n$ symbols there is a Latin square on these symbols which differs from the array in every cell. We characterise all unavoidable square arrays with at most 2 symbols, and all unavoidable arrays of order at most 4. We also identify a number of general families of unavoidable arrays, which we conjecture to be a complete account of unavoidable arrays. Next, we investigate arrays with multiple entries in each cell, and identify a number of families of unavoidable multiple entry arrays. We also discuss fractional Latin squares, and their connections to unavoidable arrays. We note that when rephrasing our results as edge list-colourings of complete bipartite graphs, we have a situation where the lists of available colours are shorter than the length guaranteed by Galvin's theorem to allow proper colourings.
%U http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/195