A dichotomy for minimum cost graph homomorphisms

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A dichotomy for minimum cost graph homomorphisms

For graphs G and H, a mapping f : V (G)→V (H) is a homomorphism 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 ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed graph H, we have the minimum cost homomorphism problem, written as MinHOM(H). The problem is to decide, for an input graph G with co...

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Let H be a fixed graph without loops. We prove that if H is a co-circular arc bigraph then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm; otherwise the minimum cost homomorphism problem to H is known to be not approximable. This solves a problem posed in an earlier paper. For the purposes of the approximation, we provide a new charact...

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 2008

ISSN: 0195-6698

DOI: 10.1016/j.ejc.2007.11.012