Hamilton decompositions of complete graphs with a 3-factor leave Original Research Article

We show that for any 2-factor U of Kn with n even, there exists a 3-factor T of Kn such that E(U)⊂E(T) such that Kn−E(T) admits a hamilton decomposition. This is proved with the method of amalgamations (graph homomorphisms), using a new result that concerns graph decompositions that are fairly divided, but not necessarily regular.