Hamilton Decomposable Graphs with Specified Leaves.

In this paper, a simple proof is given of a result that provides necessary and sufficient conditions for the existence of a hamilton decomposition ofG-E(H) for any non-bipartiter-regular complete multipartite graphGand for any 2-factorHofG. Such conditions were originally obtained by Buchanan for complete graphs (ie whenr=|V(G)|-1), and in some cases by Leach and Rodger otherwise (Leach and Rodger also settled the bipartite case). This result is extended to consider hamilton decompositions ofG-E(H?F), whereFis a 1-factor ofG. [ABSTRACT FROM AUTHOR]