Jakub Gajarský: Interpretations – how to speak about sparsity in dense graphs
We introduce and investigate the notion of first-order interpretation - a logical tool which allows us to define new structurally simple dense graphs out of sparse graphs and conversely allows us to study dense graphs in the context of sparse graphs. We will then discuss some recent applications of interpretations in the context of sparsity, which resulted in extensions of known results about sparse graphs to a more general setting.
