Hamilton Decomposable Graphs with Specified Leaves

Abstract.

In this paper, a simple proof is given of a result that provides necessary and sufficient conditions for the existence of a hamilton decomposition of G−E(H) for any non-bipartite r-regular complete multipartite graph G and for any 2-factor H of G. Such conditions were originally obtained by Buchanan for complete graphs (ie when r=|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 of G−E(H∪F), where F is a 1-factor of G.