Dihamiltonian Decomposition of Regular Graphs with Degree Three.

We consider the dihamiltonian decomposition problem for 3- regular graphs. A graph G is dihamiltonian decomposable if in the digraph obtained from G by replacing each edge of G as two directed edges, the set of edges are partitioned into 3 edge-disjoint directed hamiltonian cycles. We suggest some conditions for dihamiltonian decomposition of 3-regular graphs: for a 3-regular graph G , it is dihamiltonian decomposable only if it is bipartite, and it is not dihamiltonian decomposable if the number of vertices is a multiple of 4. Applying these conditions to interconnection network topologies, we investigate dihamiltonian decomposition of cube-connected cycles, chordal rings, etc.