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When the cartesian product of directed cycles is Hamiltonian

✍ Scribed by William T. Trotter Jr.; Paul Erdös

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
225 KB
Volume
2
Category
Article
ISSN
0364-9024

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✦ Synopsis

The Cartesian product of two hamiltonian graphs is always hamiltonian. For directed graphs, the analogous statement is false. We show that the Cartesian product C,,, x C, , of directed cycles is hamiltonian if and only if the greatest common divisor (g.c.d.) d of n, and n, is a t least two and there exist positive integers d,, d, so that d, + d, = d and g.c.d. (n,, d,) = g.c.d. (n,, d,) = 1. We also discuss some number-theoretic problems motivated by this result.

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