Keele Research Repository

This thesis investigates the circuits of edge-coloured complete graphs. There are various kinds of edge-coloured circuits. Amongst the most interesting are polychromatic circuits (each edge is differently coloured), alternating circuits (adjacent edges are differently coloured) and monochromatic circuits (every edge is the same colour). In the case of triangles, there are monochromatic, bichromatic (2-edge-coloured) and polychromatic triangles. This thesis is an investigation into edge-coloured complete graphs which do not contain one of the above kinds of circuits. Special emphasis is given to those edge-coloured complete graphs which do not contain one type of triangle, and those in which two types of triangle are forbidden. Where possible, the structure of these graphs is determined and a method of construction given; various types of extremal results are obtained.