We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width. Edge contractions can increase clique-width and rank-width.Using monadic second-order graph transductions to prove that certain graphs have unbounded clique-width.An alternative proof is given using vertex-minors.Taking induced topological minors preserves bounded clique-width.
['Bruno Courcelle']
Clique-width and edge contraction