Abstract
Let t be a positive integer, and let L=( l 1,…, l t ) and K=( k 1,…, k t ) be collections of nonnegative integers. A graph has a ( t, K, L) factorization if it can be represented as the edge-disjoint union of factors F 1,…, F t where, for 1⩽ i⩽ t, F i is k i -regular and at least l i -edge-connected. In this paper we consider ( t, K, L)-factorizations of complete equipartite graphs. First we show precisely when they exist. Then we solve two embedding problems: we show when a factorization of a complete σ-partite graph can be embedded in a ( t, K, L)-factorization of a complete s-partite graph, σ< s, and also when a factorization of K a, b can be embedded in a ( t, K, L)-factorization of K n, n , a, b⩽ n. Our proofs use the technique of amalgamations of graphs.
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