English

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}
}
R2 v1 2026-06-28T21:05:01.492Z