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Disjoint circuits in the cartesian product of two directed cycles

✍ Scribed by Stephen Curran

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 291 KB
Volume: 18
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190180213

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✦ Synopsis

Abstract

We show that the Cartesian product of two directed cycles Z~a~ X Z~b~ has r disjointly embedded circuits C~1~, C~2~, ⃛, C~r~ with specified knot classes knot__(C~i~) = (m~i~, n~i~), for i = 1, 2, ⃛, r, if and only if there exist relatively prime non‐negative integers m and n such that knot(C~i~) = (m, n)__, for i = 1, 2, ⃛, r, and r(am + bn) ≦ ab. We generalize this result to the Cayley digraph on a finite abelian group with a two‐element generating set.

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