8 research outputs found

    Between coloring and list-coloring: μ-coloring

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    A new variation of the coloring problem, mu-coloring, is defined in this paper. A coloring of a graph G = (V,E) is a function f: V -> N such that f(v) is different from f(w) if v is adjacent to w. Given a graph G = (V,E) and a function mu: V -> N, G is mu-colorable if it admits a coloring f with f(v)<= mu(v) for each v in V. It is proved that mu-coloring lies between coloring and list-coloring, in the sense of generalization of problems and computational complexity. Besides, the notion of perfection is extended to mu-coloring, giving rise to a new characterization of cographs. Finally, a polynomial time algorithm to solve mu-coloring for cographs is shown.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Cecowski Palacio, Mariano. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentin

    Between coloring and list-coloring: µ-coloring, Electron

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    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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