Amalgamations of factorizations of complete graphs (Q885295)

Let \(K=(k_1,\ldots,k_t)\) and \(L=(l_1,\ldots,l_t)\) be collections of nonnegative integers. A factorization of a graph into factors \(F_1,\ldots,F_t\) is called a \((t,K,L)\)-factorization if each factor \(F_i\) is a \(k_i\)-regular \(l_i\)-connected graph. Johnstone in 2000 proved a necessary and sufficient condition for existence of a \((t,K,L)\)-factorization of a complete graph \(K_n\). In this paper the author gives another proof of this result using amalgamations. He also proves a necessary and sufficient condition for existence of an embedding of a factorization of \(K_m\) in a \((t,K,L)\)-factorization of \(K_n\).