First-order interpretations of bounded expansion classes
Discrete Mathematics
2018-10-08 v1 Logic in Computer Science
Combinatorics
Logic
Abstract
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth decompositions, replacing treedepth by its dense analogue called shrubdepth.
Cite
@article{arxiv.1810.02389,
title = {First-order interpretations of bounded expansion classes},
author = {Jakub Gajarský and Stephan Kreutzer and Jaroslav Nešetřil and Patrice Ossona de Mendez and Michał Pilipczuk and Sebastian Siebertz and Szymon Toruńczyk},
journal= {arXiv preprint arXiv:1810.02389},
year = {2018}
}