### Bibliography

P K Jha, Naveen Agnihotri and Rajesh Kumar. 1996.
On edge exchanges in Hamiltonian Decompositions of
Kronecker-product graphs. *Computers
and Mathematics with Applications*. **31**(2):11-19.
#### Abstract

Let *G* be a connected graph on *n* vertices, and let
&alpha, &beta, &gamma and &delta be edge-disjoint cycles in *G*
such that *(i)* &alpha &beta (resp. &gamma, &delta) are
vertex-disjoint and *(ii)* |&alpha|+|&beta| = |&gamma|+|&delta|
= *n*, where |&alpha| denotes the length of &alpha. We say
that &alpha, &beta, &gamma and &delta yield two edge-disjoint
hamiltonian cycles by edge exchanges if the four cycles respectively
contain edges *e, f, g* and *h* such that each of
(&alpha - {*e*}) U (&beta - {*f*}) U {*g, h*} and
(&gamma - {*g*}) U (&delta -{*h*}) U {*e, f*} constitutes
a hamiltonian cycle in *G*. We show that if *G* is a
non-bipartite, hamiltonian decomposable graph on an even number
of vertices which satisfies certain conditions, then Kronecker product
of *G* and *K2* as well as Kronecker product of *G*
and an even cycle admits of a hamiltonian decomposition by means
of appropriate edge exchanges among smaller cycles in the product
graph.

*naveen@bhalu.com*