3D-grids are not transducible from planar graphs
Logic in Computer Science
2025-01-14 v1 Discrete Mathematics
Combinatorics
Abstract
We prove that the class of 3D-grids is cannot be transduced from planar graphs, and more generally, from any class of graphs of bounded Euler genus. To prove our result, we introduce a new structural tool called slice decompositions, and show that every graph class transducible from a class of graphs of bounded Euler genus is a perturbation of a graph class that admits slice decompositions.
Keywords
Cite
@article{arxiv.2501.07558,
title = {3D-grids are not transducible from planar graphs},
author = {Jakub Gajarský and Michał Pilipczuk and Filip Pokrývka},
journal= {arXiv preprint arXiv:2501.07558},
year = {2025}
}