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Hamilton decompositions of cartesian products of multicycles

✍ Scribed by Mellendorf, Stephen

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 320 KB
Volume: 24
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199701)24:1<85::aid-jgt10>3.0.co;2-q

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✦ Synopsis

We define the multicycle C (r) m as a cycle on m vertices where each edge has multiplicity r. So C (r) 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 (r) m × C (s) n be decomposed into r + s Hamilton cycles? We find some interesting characterizations of Hamilton cycles of C m × C n while answering the above question.

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