Abstract: In any 5-by-5 latin square, there are five positions, one in each row and column, whose entries are all different. These positions give what is called a transversal. Full transversals do not always exist; for example some 6-by-6 latin squares do not contain a full transversal of six positions.
Latin squares can also be viewed as proper edge-colorings of regular complete bipartite graphs. In these graphs, transversals correspond to 1-factors , called rainbow 1-factors, where each edge has a different color. From latin squares we know that edge-colored complete bipartite graphs may not have rainbow 1-factors.
Woolbright & Fu showed that edge-colored complete graphs will always have a rainbow 1-factor, and investigated a related question of Rosa on hypergraphs. El-Zanati, Plantholt, Sissokho and Spence solved this problem. We give a new result showing the existence of rainbow 1-factors for a hypergraph analog of the bipartite question.