3D-grids are not transducible from planar graphs
Year: 2025
Type: conference-paper
Abstract: We prove that the class of 3D-grids cannot be transduced from planar graphs, and more generally, from any class of graphs of bounded genus. To prove our result, we introduce a new structural tool called slice decompositions and study its properties. We show that every graph class transducible from a class of graphs of bounded genus is a perturbation of a graph class that admits slice decompositions. Moreover, we show that edge-stable graph classes that admit slice decomposition are transducible from weakly sparse graph classes that admits slice decompositions.
Institution: University of Warsaw
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: European Research Council
OpenAlex ID: W4415004470