Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Tree clustering for constraint networks (research note)
Artificial Intelligence
Bottom-up beats top-down for datalog
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Proceedings of the 30th IEEE symposium on Foundations of computer science
On the expressive power of Datalog: tools and a case study
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Equivalences Among Relational Expressions with the Union and Difference Operators
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
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Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Syntax vs. Semantics on Finite Structures
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Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
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Data exchange: getting to the core
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Homomorphism Closed vs. Existential Positive
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On preservation under homomorphisms and unions of conjunctive queries
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Preservation under extensions on well-behaved finite structures
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Homomorphism preservation theorems
Journal of the ACM (JACM)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Homomorphism preservation on quasi-wide classes
Journal of Computer and System Sciences
Explaining missing answers to SPJUA queries
Proceedings of the VLDB Endowment
European Journal of Combinatorics
Extension Preservation Theorems on Classes of Acyclic 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
NP by means of lifts and shadows
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Boundedness of monadic FO over acyclic structures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Datalog: a perspective and the potential
Datalog 2.0'12 Proceedings of the Second international conference on Datalog in Academia and Industry
When is naive evaluation possible?
Proceedings of the 32nd symposium on Principles of database systems
On the complexity of existential positive queries
ACM Transactions on Computational Logic (TOCL)
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Unions of conjunctive queries, also known as select-project-join-union queries, are the most frequently asked queries in relational database systems. These queries are definable by existential positive first-order formulas and are preserved under homomorphisms. A classical result of mathematical logic asserts that the existential positive formulas are the only first-order formulas (up to logical equivalence) that are preserved under homomorphisms on all structures, finite and infinite. The question of whether the homomorphism-preservation theorem holds for the class of all finite structures resisted solution for a long time. It was eventually shown that, unlike other classical preservation theorems, the homomorphism-preservation theorem does hold in the finite. In this article, we show that the homomorphism-preservation theorem holds also for several restricted classes of finite structures of interest in graph theory and database theory. Specifically, we show that this result holds for all classes of finite structures of bounded degree, all classes of finite structures of bounded treewidth, and, more generally, all classes of finite structures whose cores exclude at least one minor.