Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the polygon are visible from it. We completely classify such polygons, show that there are finitely many of lattice width greater than $2$, and computationally enumerate them. As an application of this classification, we prove new obstructions to graphs arising as skeleta of tropical plane curves.

中文翻译：

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所有晶格点都可见的凸晶格多边形

如果连接它们的线段上不存在其他格点，则两个格点彼此可见。在本文中，我们研究了包含一个格点的凸格子多边形，这样多边形中的所有其他格子点都可以从中看到。我们对这样的多边形进行了完全分类，表明存在有限多个格宽度大于 $2$，并通过计算枚举它们。作为这种分类的应用，我们证明了作为热带平面曲线骨架出现的图形的新障碍。