Between coloring and list-coloring: μ-coloring
A new variation of the coloring problem, μ-coloring, is defined in this paper. A coloring of a graph G = (V,E) is a function f: V → ℕ such that f(v) ≠ f(w) if v is adjacent to w. Given a graph G = (V, E) and a function μ: V → ℕ, G is μ-colorable if it admits a coloring f with f(v) ≤ μ(v) for each v...
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2011
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03817032_v99_n_p383_Bonomo http://hdl.handle.net/20.500.12110/paper_03817032_v99_n_p383_Bonomo |
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| Sumario: | A new variation of the coloring problem, μ-coloring, is defined in this paper. A coloring of a graph G = (V,E) is a function f: V → ℕ such that f(v) ≠ f(w) if v is adjacent to w. Given a graph G = (V, E) and a function μ: V → ℕ, G is μ-colorable if it admits a coloring f with f(v) ≤ μ(v) for each v ∈ V. It is proved that μ-coloring lies between coloring and list-coloring, in the sense of generalization of problems and computational complexity. Furthermore, the notion of perfection is extended to μ-coloring, giving rise to a new characterization of cographs. Finally, a polynomial time algorithm to solve μ-coloring for cographs is shown. |
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