Abstract A location function on a finite connected graph G takes as input any k -tuple of vertices (a profile) and outputs a single vertex. If G is a full y gated graph, then a target location function is defined by a predetermined vertex (the target) and outputs the unique vertex belonging to the convex closure of the profile which is closest to the target. If G is a finite tree, then any target function on G satisfies two conditions known in the literature as Pareto efficiency and replacement domination. We give a simple example to show that these two conditions do not characterize target functions on trees. A new condition, called the neighborhood condition, is introduced and we prove that target functions on trees are the only location functions satisfying Pareto efficiency, replacement domination, and the neighborhood condition.

中文翻译：

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有限树上的目标定位函数

摘要 有限连通图 G 上的位置函数将任何 k 元组顶点（轮廓）作为输入并输出单个顶点。如果 G 是一个全 y 门控图，则目标位置函数由预定顶点（目标）定义，并输出属于最接近目标的轮廓凸闭包的唯一顶点。如果 G 是一棵有限树，则 G 上的任何目标函数都满足文献中已知的两个条件，即帕累托效率和替换支配。我们举一个简单的例子来说明这两个条件不能表征树上的目标函数。引入了一种称为邻域条件的新条件，我们证明树上的目标函数是唯一满足帕累托效率、替换支配和邻域条件的位置函数。