# Transducing paths in graph classes with unbounded shrubdepth

@article{Pilipczuk2022TransducingPI, title={Transducing paths in graph classes with unbounded shrubdepth}, author={Michal Pilipczuk and Patrice Ossona de Mendez and Sebastian Siebertz}, journal={ArXiv}, year={2022}, volume={abs/2203.16900} }

Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class C can be ๐ฅ๐ฎ -transduced from a class of bounded-height trees (that is, has bounded shrubdepth ) if, and only if, from C one cannot ๐ฅ๐ฎ -transduce the class of all paths. This establishes one of the three remaining open questions posed by Blumensath and Courcelle about the ๐ฌ๐ฒ๐ฎ -transduction quasi-order, even in the stronger formโฆย

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