Hamiltonian decompositions of complete graphs

Abstract

It is well known that K 2 n + 1 can be decomposed into n edge-disjoint Hamilton cycles. A novel method for constructing Hamiltonian decompositions of K 2 n + 1 is given and a procedure for obtaining all Hamiltonian decompositions of of K 2 n + 1 is outlined. This method is applied to find a necessary and sufficient condition for a decomposition of the edge set of K r ( r ≤ 2 n) into n classes, each class consisting of disjoint paths to be extendible to a Hamiltonian decomposition of K 2 n + 1 so that each of the classes forms part of a Hamilton cycle.