Every graph class of bounded cliquewidth and unbounded linear cliquewidth contains arbitrarily large tree-like induced subgraphs that MSO-transduce all trees and FO-transduce subdivisions of all binary trees.
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Trees in graphs of large linear cliquewidth
Every graph class of bounded cliquewidth and unbounded linear cliquewidth contains arbitrarily large tree-like induced subgraphs that MSO-transduce all trees and FO-transduce subdivisions of all binary trees.