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Nondisconnecting disentanglements of amalgamated 2-factorizations of complete multipartite graphs. (English) Zbl 0994.05125
Summary: 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 \(K_{a,b}\).

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C45 Eulerian and Hamiltonian graphs
05C15 Coloring of graphs and hypergraphs
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