A simple construction gives layered-wheel-like graphs with arbitrarily large treewidth, arbitrarily large girth, and every outerstring induced subgraph of bounded treewidth, refuting Trotignon's conjecture.
On treewidth and maximum cliques
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A simple layered-wheel-like construction
A simple construction gives layered-wheel-like graphs with arbitrarily large treewidth, arbitrarily large girth, and every outerstring induced subgraph of bounded treewidth, refuting Trotignon's conjecture.