关于Erdens-Diophantine图和Diophantine地毯的注记
A note on Erdős-Diophantine graphs and Diophantine carpets
摘要：
丢番图是整数网格$\mathbb{Z}^{2}$上的一组点，其中所有相互的欧几里得距离都是整数。我们还谈到丢番图。在这种语言中，丢番图是完全丢番图。由于Erdans和Anning的一个著名定理，存在不包含在较大图中的完全丢番图。我们称之为Erdens-Diophantine图。丢番图的一个特殊类别是丢番图地毯。这些是整数网格子集的平面三角剖分。给出了Erdens-Diophantine图的一个有效构造，并刻画了Diophantine地毯的色数.
英文摘要：
A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. In this language a Diophantine figure is a complete Diophantine graph. Due to a famous theorem of Erdős and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdős-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdős-Diophantine graphs and characterize the chromatic number of Diophantine carpets.
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