Characterisations of Nowhere Dense Graphs

Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of graph classes generalising for example classes of graphs which exclude a fixed minor, have bounded degree or bounded local tree-width. In this paper we give a selfcontained introduction to the concept of nowhere dense classes of graphs focussing on the various ways in which they can be characterised. We also briefly sketch algorithmic applications these characterisations have found in the literature. 1998 ACM Subject Classification G.2.2 Graph Theory