Arcdisjoint hamiltonian paths in Cartesian products of directed cycles
Abstract
We show that if $C_1$ and $C_2$ are directed cycles (of length at least two), then the Cartesian product $C_1 \Box C_2$ has two arcdisjoint hamiltonian paths. (This answers a question asked by J. A. Gallian in 1985.) The same conclusion also holds for the Cartesian product of any four or more directed cycles (of length at least two), but some cases remain open for the Cartesian product of three directed cycles. We also discuss the existence of arcdisjoint hamiltonian paths in $2$generated Cayley digraphs on (finite or infinite) abelian groups.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 arXiv:
 arXiv:2203.11017
 Bibcode:
 2022arXiv220311017D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Group Theory
 EPrint:
 25 pages, 2 figures