Hamiltonian decompositions of complete graphs (Q795057)

The paper presents a procedure for constructing all Hamiltonian decompositions of the complete graph \(K_{2n+1}\). The technique is then applied to find a necessary and sufficient condition for a decomposition of the edge set of \(K_ r\) (\(r\leq 2n)\) into n classes, each class consisting of disjoint paths to be extendible to a Hamiltonian decomposition of \(K_{2n+1}\) so that each of the classes forms part of a Hamilton cycle.