Amalgamations of factorizations of complete graphs

Let t be a positive integer, and let K=(k1,…,kt) and L=(l1,…,lt) be collections of nonnegative integers. A (t,K,L)-factorization of a graph is a decomposition of the graph into factors F1,…,Ft such that Fi is ki-regular and li-edge-connected. In this paper, we apply the technique of amalgamations of graphs to study (t,K,L)-factorizations of complete graphs. In particular, we describe precisely when it is possible to embed a factorization of Km in a (t,K,L)-factorization of Kn.