منابع مشابه
On nowhere dense graphs
A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...
متن کاملCharacterisations of Nowhere Dense Graphs
Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of g...
متن کاملDirected nowhere dense classes of graphs
Many natural computational problems on graphs such as finding dominating or independent sets of a certain size are well known to be intractable, both in the classical sense as well as in the framework of parameterized complexity. Much work therefore has focussed on exhibiting restricted classes of graphs on which these problems become tractable. While in the case of undirected graphs, there is ...
متن کاملEnumeration for FOQueries over Nowhere Dense Graphs
We consider the evaluation of first-order queries over classes of databases that are nowhere dense. The notion of nowhere dense classes was introduced by Nešetřil and Ossona de Mendez as a formalization of classes of “sparse” graphs and generalizes many well-known classes of graphs, such as classes of bounded degree, bounded treewidth, or bounded expansion. It has recently been shown by Grohe, ...
متن کاملNeighborhood Complexity and Kernelization for Nowhere Dense Classes of Graphs
We prove that whenever G is a graph from a nowhere dense graph class C, and A is a subset of vertices of G, then the number of subsets of A that are realized as intersections of A with r-neighborhoods of vertices of G is at most f(r, ε) · |A|, where r is any positive integer, ε is any positive real, and f is a function that depends only on the class C. This yields a characterization of nowhere ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1969
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-20-2-243-247