In this paper we introduce two new geometric representations

In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now three decades after the introduction of tolerance graphs. In this paper we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane. Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms.

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