The complexity of colouring by semicomplete digraphs
SIAM Journal on Discrete Mathematics
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
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
Certifying LexBFS Recognition Algorithms for Proper Interval Graphs and Proper Interval Bigraphs
SIAM Journal on Discrete Mathematics
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Coloring of trees with minimum sum of colors
Journal of Graph Theory
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Communication: Minimum cost homomorphisms to semicomplete multipartite digraphs
Discrete Applied Mathematics
Minimum Cost Homomorphisms to Semicomplete Bipartite Digraphs
SIAM Journal on Discrete Mathematics
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
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
Finding a Maximum Planar Subset of a Set of Nets in a Channel
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hi-index | 0.04 |
For digraphs D and H, a mapping f:V(D)-V(H) is a homomorphism of D to H if uv@?A(D) implies f(u)f(v)@?A(H). For a fixed digraph H, the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomorphism problem was motivated by a real-world problem in defence logistics and was introduced in Gutin, Rafiey, Yeo and Tso (2006) [13]. If each vertex u@?V(D) is associated with costs c"i(u),i@?V(H), then the cost of the homomorphism f is @?"u"@?"V"("D")c"f"("u")(u). For each fixed digraph H, we have the minimum cost homomorphism problem forH and denote it as MinHOM(H). The problem is to decide, for an input graph D with costs c"i(u),u@?V(D),i@?V(H), whether there exists a homomorphism of D to H and, if one exists, to find one of minimum cost. Although a complete dichotomy classification of the complexity of MinHOM(H) for a digraph H remains an unsolved problem, complete dichotomy classifications for MinHOM(H) were proved when H is a semicomplete digraph Gutin, Rafiey and Yeo (2006) [10], and a semicomplete multipartite digraph Gutin, Rafiey and Yeo (2008) [12,11]. In these studies, it is assumed that the digraph H is loopless. In this paper, we present a full dichotomy classification for semicomplete digraphs with possible loops, which solves a problem in Gutin and Kim (2008) [9].