The grad of a graph and classes with bounded expansion

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). We generalize to these classes some results proved for proper minor closed classes and bounded degree graphs, such as the existence of low tree-width colorings and homomorphism dualities.

Jaroslav Nesetril, Patrice Ossona de Mendez. The grad of a graph and classes with bounded expansion. 7th International Colloquium on Graph Theory, 2005, Hyeres, France. pp.101-106, ⟨10.1016/j.endm.2005.06.018⟩. ⟨hal-00014741⟩