Cutwidth is a parameter used in many layout problems. Determining the cutwidth of a graph is an NP-complete problem, but it is possible to design efficient branch-andbound algorithms if good lower bounds are available for cutting branches during exploration. Knowing how to quickly evaluate good bounds in each node of the search tree is therefore crucial.

In this article, we give new lower bounds based on different graph density parameters. In particular, we give bounds using the notion of traffic grooming on a path network, which appear to be in many cases better than bounds in the literature. Furthermore, the bounds based on grooming can be computed quickly and so are of interest to design faster branchand-bound algorithms.