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 Ka,b − E(U) for any 2-factor U of Ka,b. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 460–467, 2001