Hyper-Hamiltonian Laceability of Cartesian Products of Cycles and Paths

Abstract

Abstract Let $H$ be a cartesian product graph of even cycles and paths, where the first multiplier is an even cycle of length at least $4$ and the second multiplier is a path with at least two nodes or an even cycle. Then $H$ is an equitable bipartite graph, which takes the torus, the column-torus and the even $k$-ary $n$-cube as its special cases. For any node $w$ of $H$ and any two different nodes $u$ and $v$ in the partite set of $H$ not containing $w$, an algorithm was introduced to construct a hamiltonian path connecting $u$ and $v$ in $H-w$.