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When the cartesian product of two directed cycles is hypo-Hamiltonian

✍ Scribed by Laurence E. Penn; David Witte

Publisher: John Wiley and Sons
Year: 1983
Tongue: English
Weight: 150 KB
Volume: 7
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190070409

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✦ Synopsis

We show that the Cartesian product Z, x Z, of two directed cycles is hypo-Hamiltonian (Hamiltonian) if and only if there is a pair of relatively prime positive integers m and n with ma + nb = ab -1 (ma + nb = ab). The result for hypo-Hamiltonian is new; that for Hamiltonian is known. These are special cases of the fact that there is a simple circuit of length p in Z, x Z, if and only if there is a pair of relatively prime non-negative integers m and n with ma + nb = p < ab.

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