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The Dichotomy of List Homomorphisms for Digraphs
"... The DichotomyConjecture for Constraint Satisfaction Problems has been verified for conservative problems (or, equivalently, for list homomorphism problems) by Andrei Bulatov. An earlier case of this dichotomy, for list homomorphisms to undirected graphs, came with an elegant structural distinction b ..."
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polymorphisms relevant in Bulatov’s dichotomy classification. The key concept we introduce is that of a digraph asteroidal triple (DAT). The dichotomy then takes the following form. If a digraph H has a DAT, then the list homomorphism
List Homomorphisms to reflexive digraphs
"... We study list homomorphism problems LHOM(H) for the class of reflexive digraphs H (digraphs in which each vertex has a loop). These problems have been intensively studied in the case of undirected graphs H, and appear to be more difficult for digraphs. However, it is known that each problem LHOM(H ..."
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We study list homomorphism problems LHOM(H) for the class of reflexive digraphs H (digraphs in which each vertex has a loop). These problems have been intensively studied in the case of undirected graphs H, and appear to be more difficult for digraphs. However, it is known that each problem L
Minimum Cost Homomorphisms to Digraphs
, 2009
"... 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 nonnegative integer costs. The cost of the homomorphism f of D to H is ∑ u∈V (D) c f(u)(u). The minimum cost ..."
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cost homomorphism for a fixed digraph H, denoted by MinHOM(H), asks whether or not an input digraph D, with nonnegative integer 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. Our interest is in proving a dichotomy for minimum
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Minimum Cost Homomorphisms of Digraphs
, 2005
"... 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 directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We s ..."
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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 directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We
Minimum Cost and List Homomorphisms to Semicomplete Digraphs
 Discrete Appl. Math
"... 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). Let H be a fixed directed or undirected graph. The homomorphism problem for H asks whether a directed or undirected graph input digraph D admits a homomorphism to H. The list homomorphis ..."
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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). Let H be a fixed directed or undirected graph. The homomorphism problem for H asks whether a directed or undirected graph input digraph D admits a homomorphism to H. The list
Minimum Cost Homomorphisms to reflexive digraphs
 8th Latin American Theoretical Informatics (LATIN), Rio de Janeiro, Brazil
"... For digraphs G and H, a homomorphism of G to H is a mapping f: V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). If moreover each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is u∈V (G) c f(u)(u). For each fixed digraph H, the minimum cost hom ..."
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Cited by 13 (7 self)
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digraph H which does not admit a MinMax ordering, the minimum cost homomorphism problem is NPcomplete. Thus we obtain a full dichotomy classification of the complexity of minimum cost homomorphism problems for reflexive digraphs. 1
Results 1  10
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