How many F's are there in G?

Authors:
Jaroslav Nešetřil;Patrice Ossona de Mendez
Affiliations:
Department of Applied Mathematics, and Institute for Theoretical Computer Science, Charles University, Prague, Czech Republic;Centre d'Analyse et de Mathématique Sociales, Centre National de la Recherche Scientifique & íícole des Hautes ítudes en Sciences Sociales, Paris, France
Venue:
European Journal of Combinatorics
Year:
2011

Citing 7
Cited 2

Invitation to Discrete Mathematics

Invitation to Discrete Mathematics
Linear time low tree-width partitions and algorithmic consequences

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tree-depth, subgraph coloring and homomorphism bounds

European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions

European Journal of Combinatorics
Grad and classes with bounded expansion II. Algorithmic aspects

European Journal of Combinatorics
On nowhere dense graphs

European Journal of Combinatorics
Finite model theory on tame classes of structures

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science

On nowhere dense graphs

European Journal of Combinatorics
Characterisations and examples of graph classes with bounded expansion

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that the asymptotic logarithmic density of copies of a graph F in the graphs of a nowhere dense class C is integral and we determine the range of its possible values. This leads to a generalization of the trichotomy theorem of Nesetril and Ossona de Mendez (2011) [18] and to a notion of the degree of freedom of a graph F in a class C. This provides yet another formulation of the somewhere dense-nowhere dense classification. We obtain a structural result concerning the asymptotic shape of graphs with given degree of freedom.