For each m≥1, consider the graph Gm whose vertex set is the set N={0,1,2,…} of natural numbers and whose edges are the pairs xy with y=x+m or y=x-m or y=mx or y=x/m. Our aim in this note is to show that, for each m, the graph Gm contains a Hamilton path. This answers a question of Lichiardopol.
Paper (pdf)