Generalized Latin rectangles I: Construction and decomposition

A (p, q, x)-latin rectangle is a rectangular matrix with x symbols in each cell such that each symbol occurs at most p times in each row and at most q times in each column. We exploit the close correspondence between (p, q, x)-latin rectangles and equitable edge-colourings of certain graphs. This paper contains results on existence and various forms of decomposition of such rectangles. In a sequel paper embedding is considered.