A graph coloring algorithm for large scale scheduling problems
Computers and Operations Research
Absolute retracts of bipartite graphs
Discrete Applied Mathematics
The complexity of colouring by semicomplete digraphs
SIAM Journal on Discrete Mathematics
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Chromatically optimal rigid graphs
Journal of Combinatorial Theory Series B
The effect of two cycles on the complexity of colouring by directed graphs
Discrete Applied Mathematics
On the complexity of type inference with coercion
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Efficient characterizations of n-chromatic absolute retracts
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics
Precoloring extension. I: Interval graphs
Discrete Mathematics - Special volume (part 1) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs”
Algorithmic aspects of type inference with subtypes
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the complexity of colouring by superdiagraphs of bipartite graphs
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Absolute reflexive retracts and absolute bipartite retracts
Discrete Applied Mathematics
Characterising tractable constraints
Artificial Intelligence
Gro¨tzsch's 3-color theorem and its counterparts for the torus and the projective plane
Journal of Combinatorial Theory Series B
Hereditarily hard H-colouring problems
Selected papers of the 14th British conference on Combinatorial conference
Handbook of combinatorics (vol. 2)
Complexity of tree homomorphisms
Discrete Applied Mathematics
Satisfiability of inequalities in a poset
Fundamenta Informaticae - Special issue: to the memory of Prof. Helena Rasiowa
Closure properties of constraints
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Constraint satisfaction and database theory: a tutorial
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The complexity of H-colouring of bounded degree graphs
Discrete Mathematics
Duality theorems for finite structures (characterising gaps and good characterisations)
Journal of Combinatorial Theory Series B
A graph formulation of a school scheduling algorithm
Communications of the ACM
Finding skew partitions efficiently
Journal of Algorithms
Colorings and homomorphisms of degenerate and bounded degree graphs
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Classification of Homomorphisms to Oriented Cycles and of k-Partite Satisfiability
SIAM Journal on Discrete Mathematics
Computational Complexity of Compaction to Reflexive Cycles
SIAM Journal on Computing
A Fourier-theoretic perspective on the Condorcet paradox and Arrow's theorem
Advances in Applied Mathematics
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
A combinatorial algorithm for MAX CSP
Information Processing Letters
SIAM Journal on Discrete Mathematics
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The Complexity of the Extendibility Problem for Finite Posets
SIAM Journal on Discrete Mathematics
Acyclic Homomorphisms and Circular Colorings of Digraphs
SIAM Journal on Discrete Mathematics
On sparse graphs with given colorings and homomorphisms
Journal of Combinatorial Theory Series B
The list partition problem for graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Dichotomies for classes of homomorphism problems involving unary functions
Theoretical Computer Science
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Generalized Majority-Minority Operations are Tractable
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A polynomial-time algorithm for near-unanimity graphs
Journal of Algorithms
Short Answers to Exponentially Long Questions: Extremal Aspects of Homomorphism Duality
SIAM Journal on Discrete Mathematics
A Dichotomy Theorem on Fixed Points of Several Nonexpansive Mappings
SIAM Journal on Discrete Mathematics
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
H-Coloring dichotomy revisited
Theoretical Computer Science - Graph colorings
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
Full Constraint Satisfaction Problems
SIAM Journal on Computing
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Journal of Combinatorial Theory Series B
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Tractability and learnability arising from algebras with few subpowers
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
A dualistic approach to bounding the chromatic number of a graph
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Grad and classes with bounded expansion II. Algorithmic aspects
European Journal of Combinatorics
SIAM Journal on Discrete Mathematics
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
European Journal of Combinatorics
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Forbidden lifts (NP and CSP for combinatorialists)
European Journal of Combinatorics
Grad and classes with bounded expansion III. Restricted graph homomorphism dualities
European Journal of Combinatorics
Projectivity and independent sets in powers of graphs
Journal of Graph Theory
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Journal of Graph Theory
Near-Unanimity Functions and Varieties of Reflexive Graphs
SIAM Journal on Discrete Mathematics
Minimum Cost Homomorphism Dichotomy for Locally In-Semicomplete Digraphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Communication: Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
Communication: Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The Ramsey number R(3, t) has order of magnitude t2/log t
Random Structures & Algorithms
Dualities in full homomorphisms
European Journal of Combinatorics
A combinatorial constraint satisfaction problem dichotomy classification conjecture
European Journal of Combinatorics
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
Advances on the list stubborn problem
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Efficient enumeration for conjunctive queries over x-underbar structures
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
Note: The Ck-extended graft construction
Discrete Applied Mathematics
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds on the approximability of almost-satisfiable Horn SAT and exact hitting set
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The dichotomy of list homomorphisms for digraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
Graph partitions with prescribed patterns
European Journal of Combinatorics
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Constraint satisfaction problems have enjoyed much attention since the early seventies, and in the last decade have become also a focus of attention amongst theoreticians. Graph colourings are a special class of constraint satisfaction problems; they offer a microcosm of many of the considerations that occur in constraint satisfaction. From the point of view of theory, they are well known to exhibit a dichotomy of complexity - the k-colouring problem is polynomial-time solvable when k@?2, and NP-complete when k=3. Similar dichotomy has been proved for the class of graph homomorphism problems, which are intermediate problems between graph colouring and constraint satisfaction. However, for general constraint satisfaction problems, dichotomy has only been conjectured. Although the conjecture remains unproven to this day, it has been driving much of the theoretical research on constraint satisfaction problems, which combines methods of logic, universal algebra, analysis, and combinatorics. Currently, this is a very active area of research, and it is our goal here to present some of the recent developments, updating some of the information in existing books and surveys, while focusing on both the mathematical and the computational aspects of the theory. Given the level of activity, we are only able to survey a fraction of the new work, with emphasis on our own areas of interest.