# Arc-disjoint hamiltonian paths in Cartesian products of directed cycles

@inproceedings{Darijani2022ArcdisjointHP, title={Arc-disjoint hamiltonian paths in Cartesian products of directed cycles}, author={Iren Darijani and Babak Miraftab and Dave Witte Morris}, year={2022} }

. We show that if C 1 and C 2 are directed cycles (of length at least two), then the Cartesian product C 1 (cid:3) C 2 has two arc-disjoint 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 arc-disjoint hamiltonian paths in 2-generated Cayley…

## One Citation

### Hamiltonicity in generalized quasi-dihedral groups

- Mathematics
- 2022

Witte Morris showed in [21] that every connected Cayley graph of a ﬁnite (generalized) dihedral group has a Hamiltonian path. The inﬁnite dihedral group is deﬁned as the free product with…

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