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Pré-Publication, Document De Travail Année : 2007

Probabilistic graph-coloring in bipartite and split graphs

Résumé

We revisit in this paper the stochastic model for minimum graph-coloring introduced in (C. Murat and V. Th. Paschos, On the probabilistic minimum coloring and minimum k-coloring, Discrete Applied Mathematics 154, 2006), and study the underlying combinatorial optimization problem (called probabilistic coloring) in bipartite and split graphs. We show that the obvious 2-coloring of any connected bipartite graph achieves standardapproximation ratio 2, that when vertex-probabilities are constant probabilistic coloring is polynomial and, finally, we propose a polynomial algorithm achieving standardapproximation ratio 8/7. We also handle the case of split graphs. We show that probabilistic coloring is NP-hard, even under identical vertex-probabilities, that it is approximable by a polynomial time standard-approximation schema but existence of a fully a polynomial time standard-approximation schema is impossible, even for identical vertex-probabilities, unless P = NP. We finally study differential-approximation of probabilistic coloring in both bipartite and split graphs.
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Dates et versions

hal-00909484 , version 1 (26-11-2013)

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  • HAL Id : hal-00909484 , version 1

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Nicolas Bourgeois, Federico Della Croce, Bruno Escoffier, Cecile Murat, Vangelis Paschos. Probabilistic graph-coloring in bipartite and split graphs. 2007. ⟨hal-00909484⟩
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