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For graphs G and H, a mapping f : V (G)→V (H) is a homomor-phism of G to H if uv ∈ E(G) implies f (u)f (v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs c i (u), i ∈ V (H), then the cost of the homomorphism f is u∈V (G) c f (u) (u). For each fixed graph H, we have the minimum cost homomorphism problem, written as MinHOM(H). The(More)
The increasing availability of network data is creating a great potential for knowledge discovery from graph data. In many applications, feature vectors are given in addition to graph data, where nodes represent entities, edges relationships between entities, and feature vectors associated with the nodes represent properties of entities. Often features and(More)
Level of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies , sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and(More)
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 homomorphism problem for H is a generalization of the homomorphism(More)
Let G be an input graph with n vertices and m edges and let k be a fixed parameter. We provide a single exponential FPT algorithm with running time O(c k n(n+m)), c = min{18, k} that turns graph G into an interval graph by deleting at most k vertices from G. This solves an open problem posed by Marx [19]. We also provide a single exponential FPT algorithm(More)
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 c i (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 homomorphism problem for H, denoted MinHOM(H), is the(More)
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 study an optimization version of this decision problem.(More)
An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edge-colored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C 0 and a (possibly empty) collection of properly colored(More)
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). If, moreover, 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 homomor-phism problem for H. The problem is to(More)