Nondisconnecting disentanglements of amalgamated 2‐factorizations of complete multipartite graphs

In this paper necessary and sufficient conditions are found for an edge‐colored graph H to be the homomorphic image of a 2‐factorization of a complete multipartite graph G in which each 2‐factor of G has the same number of components as its corresponding color class in H. This result is used to completely solve the problem of finding hamilton decompositions of K_a,b ? E(U) for any 2‐factor U of K_a,b. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 460–467, 2001