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We define the multicycle C m as a cycle on m vertices where each edge has multiplicity r. So C m can be decomposed into r Hamilton cycles. We provide a complete answer to the following question: for which positive integers m, n, r, s with m, n ≥ 3 can the Cartesian product of two multicycles C m × C n be decomposed into r + s Hamilton cycles? We find some interesting characterizations of Hamilton cycles of Cm ×Cn while answering the above question. c © 1997 John Wiley & Sons, Inc.

Hamilton decompositions of cartesian products of multicycles