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
The restrictive H-coloring problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Recognizing frozen variables in constraint satisfaction problems
Theoretical Computer Science
Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
Representation characterizations of chordal bipartite graphs
Journal of Combinatorial Theory Series B
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
Majority constraints have bounded pathwidth duality
European Journal of Combinatorics
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Extension problems with degree bounds
Discrete Applied Mathematics
The restrictive H-coloring problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Discrete Applied Mathematics
Computational complexity of generalized domination: a complete dichotomy for chordal graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Bounded tree-width and CSP-related problems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Complexity of conservative constraint satisfaction problems
ACM Transactions on Computational Logic (TOCL)
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
Computing vertex-surjective homomorphisms to partially reflexive trees
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
The dichotomy of list homomorphisms for digraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Interval graphs, adjusted interval digraphs, and reflexive list homomorphisms
Discrete Applied Mathematics
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
Approximation of minimum cost homomorphisms
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On the approximation of minimum cost homomorphism to bipartite graphs
Discrete Applied Mathematics
Graph partitions with prescribed patterns
European Journal of Combinatorics
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Given graphs G, H, and lists L(v) ⊆ V(H), v ε V(G), a list homomorphism of G to H with respect to the lists L is a mapping f : V(G) → V(H) such that uv ε E(G) implies f(u)f(v) ε E(H), and f(v) ε L(v) for all v ε V(G). The list homomorphism problem for a fixed graph H asks whether or not an input graph G, together with lists L(v) ⊆ V(H), v ε V(G), admits a list homomorphism with respect to L. In two earlier papers, we classified the complexity of the list homomorphism problem in two important special cases: When H is a reflexive graph (every vertex has a loop), the problem is polynomial time solvable if H is an interval graph, and is NP-complete otherwise. When H is an irreflexive graph (no vertex has a loop), the problem is polynomial time solvable if H is bipartite and $\overline{H}$ is a circular arc graph, and is NP-complete otherwise. In this paper, we extend these classifications to arbitrary graphs H (each vertex may or may not have a loop). We introduce a new class of graphs, called bi-arc graphs, which contains both reflexive interval graphs (and no other reflexive graphs), and bipartite graphs with circular arc complements (and no other irreflexive graphs). We show that the problem is polynomial time solvable when H is a bi-arc graph, and is NP-complete otherwise. In the case when H is a tree (with loops allowed), we give a simpler algorithm based on a structural characterization. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 61–80, 2003