Some equitably 3-colourable cycle decompositions of complete equipartite graphs Original Research Article

Let image be a graph in which each vertex has been coloured using one of image colours, say image. If an image-cycle image in image has image vertices coloured image, image, and image for any image, then image is said to be equitably image-coloured. An image-cycle decomposition image of a graph image is equitably image-colourable if the vertices of image can be coloured so that every image-cycle in image is equitably image-coloured. For image 3, 4 and 5 we completely settle the existence question for equitably 3-colourable image-cycle decompositions of complete equipartite graphs.