# Treewidth of monotone graph classes with bounded cliquewidth

Assume a graph class excludes a certain bicique $$K_{n,n}$$ and has bounded cliquewidth. Then by a result of Gurski and Wanke, this class also has bounded treewidth. Is there a similar result that states the following: Every graph class with bounded cliquewidth that is monotone (i.e., closed under removing edges and vertices) has bounded treewidth?