Hamilton decompositions of balanced complete multipartite graphs with primitive leaves

A graph G is said to be primitive if it contains no proper factors. In this paper, by using the amalgamation technique, we find sufficient conditions for the existence of a d -regular graph G on n vertices which: 1. Hamilton decomposition, and complement in K m p that is primitive. general results are then used to consider the bounds on m when p and d are fixed. The case p = 6 for all m and d is considered in more detail.