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
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Foundations of Databases: The Logical Level
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Syntax vs. Semantics on Finite Structures
Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Proceedings of the 12th International Workshop on Computer Science Logic
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
Parameterized Complexity
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
European Journal of Combinatorics
Preservation under extensions on well-behaved finite structures
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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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 existential positive formulas are the only first-order formulas (up to logical equivalence) that are preserved under homomorphisms on all structures, finite and infinite. It is long-standing open problem in finite model theory, however, to determine whether the same homomorphism-preservation result holds in the finite, that is, whether every first-order formula preserved under homomorphisms on finite structures is logically equivalent to an existential positive formula on finite structures. In this paper, we show that the homomorphism-preservation theorem holds for several large 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.