Treewidth t+1 graphs are not first-order transducible from treewidth t graphs, with analogous separations for Hadwiger number and for treewidth 4 graphs from planar graphs.
3D-grids are not transducible from planar graphs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
cs.LO 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
First-order transducibility among classes of sparse graphs
Treewidth t+1 graphs are not first-order transducible from treewidth t graphs, with analogous separations for Hadwiger number and for treewidth 4 graphs from planar graphs.