par Joret, Gwenaël ;Micek, Piotr;Ossona de Mendez, Patrice;Wiechert, V.
Référence Combinatorica, 39, 5, page (1055-1079)
Publication Publié, 2019-07-01
Article révisé par les pairs
Résumé : Nowhere dense graph classes provide one of the least restrictive notions of sparsity for graphs. Several equivalent characterizations of nowhere dense classes have been obtained over the years, using a wide range of combinatorial objects. In this paper we establish a new characterization of nowhere dense classes, in terms of poset dimension: A monotone graph class is nowhere dense if and only if for every h⩾1 and every ε > 0, posets of height at most h with n elements and whose cover graphs are in the class have dimension O(nϵ).