Grad and classes with bounded expansion I. Decompositions

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

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Jaroslav Nesetril, Patrice Ossona de Mendez
• Keywords: Average Density, EJC 2007, EJC 2008, Information Technology, Low Tree-depth Colorings, Such Classes