Abstract

In this thesis the closely related problems of embedding symmetric latin rectangles and embedding properly edge-coloured complete graphs are consider. The thesis is divided into three parts. The first part is an introduction and survey about completing partial latin squares and embedding latin rectangles. The second part is a proof of a former conjecture of Dugdale and Hilton about embedding edge-coloured complete graphs and the third and final part is a partial generalisation of the second part to the problem of embedding symmetric latin squares.