The Grad of a Graph and Classes with Bounded Expansion
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2012, Discrete Applied MathematicsCharacterisations and examples of graph classes with bounded expansion
2012, European Journal of CombinatoricsCitation Excerpt :Yet in several aspects, the new graph inherits the structure of the original. A further generalisation consists in classes of graphs having bounded expansion, as introduced by Nešetřil and Ossona de Mendez [56,57,59]. Roughly speaking, these classes are defined by the fact that the maximum average degree of a shallow minor of a graph in the class is bounded by a function of the depth of the shallow minor.
How many F's are there in G?
2011, European Journal of CombinatoricsCitation Excerpt :A general view of the integration of usual sparse classes within this classification scheme is presented in Fig. 2. In this figure there appear in particular bounded expansion classes which were defined by the authors in [10,9,12,11,14], and almost wide and quasi-wide classes which were defined by Atserias et al. in a model theory context (cf. [2] for instance). The trichotomy theorem which we recall now was the first attempt at a classification of classes of graphs.
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2009, European Journal of CombinatoricsCitation Excerpt :Kierstead, Trotter [11] We review some definitions and notation introduced in [17–20]: Now we shall replace the acyclicity condition by a transitivity condition.