English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 arc-disjoint hamiltonianpaths. (This answers a question asked by J. A. Gallian in 1985.) The sameconclusion also holds for the Cartesian product of any four or more directedcycles (of length at least two), but some cases remain open for the Cartesianproduct of three directed cycles.  We also discuss the existence of arc-disjoint hamiltonian paths in$2$-generated Cayley digraphs on (finite or infinite) abelian groups.

Arc-disjoint hamiltonian paths in Cartesian products of directed cycles