Amalgamations of factorizations of complete graphs

Let t be a positive integer, and let K = ( k 1 , … , k t ) and L = ( l 1 , … , l t ) be collections of nonnegative integers. A ( t , K , L ) -factorization of a graph is a decomposition of the graph into factors F 1 , … , F t such that F i is k i -regular and l i -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 K m in a ( t , K , L ) -factorization of K n .