2007/03/01 by Martin Grohe · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Optimization and Search Problems #Homomorphism #Parameterized complexity #Constraint satisfaction problem #Discrete mathematics #Mathematics #Equivalence (formal languages) #Homomorphic encryption #Bounded function #Complexity of constraint satisfaction #Algebra homomorphism #Constraint (computer-aided design) #Characterization (materials science) #Constraint satisfaction #Combinatorics #Computer science #Local consistency
paper · doi:10.1145/1206035.1206036
openalex publication_date 2007/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/06
We give a complexity theoretic classification of homomorphism problems for graphs and, more generally, relational structures obtained by restricting the left hand side structure in a homomorphism. For every class C of structures, let HOM(C,−) be the problem of deciding whether a given structure A ∈C has a homomorphism to a given (arbitrary) structure ß. We prove that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C,−) is in polynomial time if and only if C has bounded tree width modulo homomorphic equivalence. Translated into the language of constraint satisfaction problems, our result yields a characterization of the tractable structural restrictions of constraint satisfaction problems. Translated into the language of database theory, it implies a characterization of the tractable instances of the evaluation problem for conjunctive queries over relational databases.