On December 10, 2019, Jakub Gajarský from Technische Universität Berlin presented a talk on the class of graphs of structurally bounded expansion and its relationship to the low shrubdepth covers. The title of his talk was “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.