ar X iv : m at h . C O / 0 50 83 23 v 1 1 7 A ug 2 00 5 GRAD AND CLASSES WITH BOUNDED EXPANSION

Abstract

We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, ∇r(G). For these classes we prove the existence of several partition results such as the existence of low tree-width and low treedepth colorings. This generalizes and simplifies several earlier results (obtained for minor closed classes).

Cite this paper

@inproceedings{Nesetril2006arXI, title={ar X iv : m at h . C O / 0 50 83 23 v 1 1 7 A ug 2 00 5 GRAD AND CLASSES WITH BOUNDED EXPANSION}, author={Jaroslav Nesetril and Patrice Ossona de Mendez}, year={2006} }