On the complexity of H-coloring
Journal of Combinatorial Theory Series B
A simple proof of the multiplicativity of directed cycles of prime power length
Discrete Applied Mathematics
The Existence of Homomorphisms to Oriented Cycles
SIAM Journal on Discrete Mathematics
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
Classification of Homomorphisms to Oriented Cycles and of k-Partite Satisfiability
SIAM Journal on Discrete Mathematics
Minimizing Average Completion of Dedicated Tasks and Interval Graphs
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Coloring of trees with minimum sum of colors
Journal of Graph Theory
Communication: Minimum cost homomorphisms to semicomplete multipartite digraphs
Discrete Applied Mathematics
Minimum Cost Homomorphism Dichotomy for Oriented Cycles
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Minimum Cost Homomorphism Dichotomy for Locally In-Semicomplete Digraphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Minimum Cost Homomorphisms to Semicomplete Bipartite Digraphs
SIAM Journal on Discrete Mathematics
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Precoloring extension on unit interval 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
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For digraphs D and H, a homomorphism of D to H is a mapping f: V(D)→V(H) such that uv ∈ A(D) implies f(u)f(v) ∈ A(H). Suppose D and H are two digraphs, and ci(u), u ∈ V(D), i ∈ V(H), are non-negative real costs. The cost of the homomorphism f of D to H is Σu∈V(D)cf(u)(u). The minimum cost homomorphism for a fixed digraph H, denoted by MinHOM(H), asks whether or not an input digraph D, with nonnegative real costs ci(u), u ∈ V(D), i ∈ V(H), admits a homomorphism f to H and if it admits one, find a homomorphism of minimum cost. The minimum cost homomorphism problem seems to offer a natural and practical way to model many optimization problems such as list homomorphism problems, retraction and precolouring extension problems, chromatic partition optimization, and applied problems in repair analysis. Our interest is in proving a dichotomy for minimum cost homomorphism problem: we would like to prove that for each digraph H, MinHOM(H) is polynomial-time solvable, or NP-hard. We say that H is a digraph with some loops, if H has at least one loop. For reflexive digraphs H (every vertex has a loop) the complexity of MinHOM(H) is well understood. In this paper, we obtain a full dichotomy for MinHOM(H) when H is an oriented cycle with some loops. Furthermore, we show that this dichotomy is a remarkable progress toward a dichotomy for oriented graphs with some loops.