Grad and classes with bounded expansion I. decompositions

Jaroslav Nesetril (1) , Patrice Ossona de Mendez (2)

1 KAM - Department of Applied Mathematics (KAM)
2 CAMS - Centre d'Analyse et de Mathématique sociales

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 tree-depth colorings. This generalizes and simplifies several earlier results (obtained for minor closed classes).

Domaines: Combinatoire [math.CO]

Jaroslav Nesetril, Patrice Ossona de Mendez. Grad and classes with bounded expansion I. decompositions. European Journal of Combinatorics, 2008, 29 (3), pp.760-776. ⟨10.1016/j.ejc.2006.07.013⟩. ⟨hal-00260721⟩