# Is clique-width preserved under edge contractions?

Let $G$ be class of graphs with bounded clique-width. In each graph in $G$ some edges are contracted (e.g. randomly). Is now the clique-width still bounded?

In case it is (in general) no longer bounded, I would be very interested in a counter-example.

This may be a pre-answer: in this 2007 arXiv paper (Problem 4.9), it is stated as an open problem whether one can find a graph $G$ and an edge $\{x,y\} \in E(G)$ such that $cw(G) < cw(G^{x,y})$, where $G^{x,y}$ is the graph $G$ with edge $\{x,y\}$ contracted.