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The notion of nowhere dense graph classes was introduced by Ne\v{s}et\v{r}iland Ossona de Mendez and provides a robust concept of uniform sparseness ofgraph classes. Nowhere dense classes generalize many familiar classes of sparsegraphs such as classes that exclude a fixed graph as a minor or topologicalminor. They admit several seemingly unrelated natural characterizations thatlead to strong algorithmic applications. In particular, the model-checkingproblem for first-order logic is fixed-parameter tractable over these classes.These notes, prepared for a tutorial at Highlights of Logic, Games and Automata2019, are a brief introduction to the theory of nowhere denseness, driven byalgorithmic applications.

Nowhere dense graph classes and algorithmic applications. A tutorial at Highlights of Logic, Games and Automata 2019