Interpreting nowhere dense graph classes as a classical notion of model theory

Authors:
Hans Adler;Isolde Adler
Affiliations:
-;-
Venue:
European Journal of Combinatorics
Year:
2014

Citing 4
Cited 0

A shorter model theory

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Homomorphism preservation on quasi-wide classes

Journal of Computer and System Sciences
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

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Abstract

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of complete graphs that occur as r-minors. We observe that this recent tameness notion from (algorithmic) graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property. Expressed in terms of PAC learning, the concept classes definable in first-order logic in a subgraph-closed graph class have bounded sample complexity, if and only if the class is nowhere dense.