Grad and classes with bounded expansion I. Decompositions

Authors:
Jaroslav Nešetřil;Patrice Ossona de Mendez
Affiliations:
Department of Applied Mathematics, Charles University, Malostranské nám.25, 11800 Praha 1, Czech Republic and Institute of Theoretical Computer Science (ITI), Charles University, Malostr ...;Centre d'Analyse et de Mathématiques Sociales, CNRS, UMR 8557, 54 Bd Raspail, 75006 Paris, France
Venue:
European Journal of Combinatorics
Year:
2008

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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) ofGwith rankr, @?"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).