First-Order Interpretations of Bounded Expansion Classes
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.
Logical interpretations/transductions
structurally sparse graphs
bounded expansion
Theory of computation~Logic
Theory of computation~Finite Model Theory
126:1-126:14
Regular Paper
Jakub
Gajarský
Jakub Gajarský
Technical University Berlin, Germany
J. Gajarský and S. Kreutzer are supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Consolidator Grant DISTRUCT, grant agreement No 648527).
Stephan
Kreutzer
Stephan Kreutzer
Technical University Berlin, Germany
Jaroslav
Nesetril
Jaroslav Nesetril
Charles University, Prague, Czech Republic
J. Nešetřil and P. Ossona de Mendez are supported by CE-ITI P202/12/G061 of GACR and European Associated Laboratory (LEA STRUCO).
Patrice
Ossona de Mendez
Patrice Ossona de Mendez
CAMS (CNRS, UMR 8557), Paris, France
Michal
Pilipczuk
Michal Pilipczuk
University of Warsaw, Warsaw, Poland
\begin{minipage}[t][1.0cm][b]{0.88\textwidth}M. Pilipczuk and S. Siebertz are supported by the National Science Centre of Poland (NCN) via POLONEZ grant agreement UMO-2015/19/P/ST6/03998, which has received funding from the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie grant agreement No. 665778).\end{minipage}\hfil\begin{minipage}[t][0.7cm][b]{0.09\textwidth}\includegraphics[width=38px]{flag_bw}\end{minipage}
Sebastian
Siebertz
Sebastian Siebertz
University of Warsaw, Warsaw, Poland
Szymon
Torunczyk
Szymon Torunczyk
University of Warsaw, Warsaw, Poland
Sz. Toru{ń}czyk is supported by the NCN grant 2016/21/D/ST6/01485.
10.4230/LIPIcs.ICALP.2018.126
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Jakub Gajarský, Stephan Kreutzer, Jaroslav Nešetřil, Patrice Ossona de Mendez, Michał Pilipczuk, Sebastian Siebertz, and Szymon Toruńczyk
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