(c-)AND：一种新的图模型
(c-)AND: A new graph model
摘要：
在本文中，我们研究了以下图模型的范围：每个顶点被分配给度量空间中的一个盒子和属于该盒子的代表元素。两个顶点被一条边连接当且仅当其各自的盒包含相反的代表元素。我们把我们的研究集中在与顶点相关的盒子（因此代表元素）在欧几里得线上传播的情况下。我们给这两个，组合和交叉表征的模型。基于这些特征，我们确定包含模型的图族（e。例如，在一个实施例中，boxicity 2 graphs）和新模型包含的其他图形（e.例如，在一个实施例中，根定向路径）。我们还研究了特定的情况下，每个代表性的元素是其各自的盒子的中心。在这种特殊的情况下，我们提供建设性的表示区间，块和外平面图。最后，我们表明，一般和特定的模型是不等价的，通过构建一个图形的家庭，分开这两种情况。
英文摘要：
In this document, we study the scope of the following graph model: each vertex is assigned to a box in a metric space 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 the Euclidean line. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
