  We show that there is a permutation $f$ of the positive integers such that
for $n \geq 2,$ l.c.m.$(f(n), f(n+1)) \leq cn(\log n)^2,$ where $c$ is a
positive constant. It improves previous results of Erd\"os, Freud and Hegyvari
(1983), and Chen and Ji (2011).
