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p-box: a new graph model

Abstract : In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.
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https://hal.inria.fr/hal-01196865
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Submitted on : Thursday, September 10, 2015 - 3:17:30 PM
Last modification on : Wednesday, May 6, 2020 - 8:18:02 PM
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Mauricio Soto, Christopher Thraves-Caro. p-box: a new graph model. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.169--186. ⟨hal-01196865⟩

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