论文标题
弧线 - 偶发性哈密顿路径在笛卡尔产物的定向周期产品中
Arc-disjoint hamiltonian paths in Cartesian products of directed cycles
论文作者
论文摘要
我们表明，如果$ c_1 $和$ c_2 $是指导循环（长度至少两个），则笛卡尔产品$ C_1 \ box C_2 $具有两个Arc-Disjoint Hamiltonian Paths。 （这回答了J. A. Gallian在1985年提出的一个问题。）同样的结论也适用于任何四个或多个定向周期的笛卡尔产品（至少两个），但有些情况仍然是三个定向周期的笛卡尔产物开放的。 我们还讨论了在$ 2 $生成的Cayley Digraphs上（有限或无限）Abelian群体中的弧线 - 偶然汉密尔顿路径的存在。
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 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 digraphs on (finite or infinite) abelian groups.
