Journal of the ACM (JACM)
Proceedings of the 30th IEEE symposium on Foundations of computer science
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Proceedings of the 12th International Workshop on Computer Science Logic
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Homomorphism preservation theorems
Journal of the ACM (JACM)
Preservation under Extensions on Well-Behaved Finite Structures
SIAM Journal on Computing
Finite model theory on tame classes of structures
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Interpreting nowhere dense graph classes as a classical notion of model theory
European Journal of Combinatorics
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A class of structures is said to have the homomorphism preservation property just in case every first-order formula that is preserved by homomorphisms on this class is equivalent to an existential-positive formula. It is known by a result of Rossman that the class of finite structures has this property and by previous work of Atserias et al. that various of its subclasses do. We extend the latter results by introducing the notion of a quasi-wide class and showing that any quasi-wide class that is closed under taking substructures and disjoint unions has the homomorphism preservation property. We show, in particular, that classes of structures of bounded expansion and classes that locally exclude minors are quasi-wide. We also construct an example of a class of finite structures which is closed under substructures and disjoint unions but does not admit the homomorphism preservation property.