@article{10.1145/3382093,
    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 transductions 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 covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.},
    Address = {New York, NY, USA},
    Author = {Gajarsk\'{y}, Jakub and Kreutzer, Stephan and Ne\v{s}ET\v{r}il, Jaroslav and Mendez, Patrice Ossona De and Pilipczuk, Micha{\l}{} and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
    ISSN = {1529-3785},
    Journal = {ACM Trans. Comput. Logic},
    Keywords = {model-checking, first-order logic, logical interpretations, Sparse graph classes, bounded expansion},
    Month = {July},
    Number = {4},
    Publisher = {Association for Computing Machinery},
    Title = {First-Order Interpretations of Bounded Expansion Classes},
    URL = {https://doi.org/10.1145/3382093},
    Volume = {21},
    Year = {2020},
    articleno = {29},
    bdsk-url-1 = {https://doi.org/10.1145/3382093},
    date-added = {2021-05-19 15:31:26 +0200},
    date-modified = {2021-05-19 15:31:26 +0200},
    issue_date = {October 2020},
    numpages = {41},
    doi = {10.1145/3382093}
}

@article{10.1145/3382093, 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 transductions 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 covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.}, Address = {New York, NY, USA}, Author = {Gajarsk\'{y}, Jakub and Kreutzer, Stephan and Ne\v{s}ET\v{r}il, Jaroslav and Mendez, Patrice Ossona De and Pilipczuk, Micha{\l}{} and Siebertz, Sebastian and Toru\'{n}czyk, Szymon}, ISSN = {1529-3785}, Journal = {ACM Trans. Comput. Logic}, Keywords = {model-checking, first-order logic, logical interpretations, Sparse graph classes, bounded expansion}, Month = {July}, Number = {4}, Publisher = {Association for Computing Machinery}, Title = {First-Order Interpretations of Bounded Expansion Classes}, URL = {https://doi.org/10.1145/3382093}, Volume = {21}, Year = {2020}, articleno = {29}, bdsk-url-1 = {https://doi.org/10.1145/3382093}, date-added = {2021-05-19 15:31:26 +0200}, date-modified = {2021-05-19 15:31:26 +0200}, issue_date = {October 2020}, numpages = {41}, doi = {10.1145/3382093} }