Antidirected Hamilton Cycles in the Cartesian Product of Directed Cycles

Abstract

We prove that the Cartesian product of two directed cycles of lengths $n_1$ and $n_2$ contains an antidirected Hamilton cycle, and hence is decomposable into antidirected Hamilton cycles, if and only if $gcd(n_1,n_2)=2$. For the Cartesian product of $k>2$ directed cycles, we establish new sufficient conditions for the existence of an antidirected Hamilton cycle.