We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W(x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits.

中文翻译：

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间隔图限制。

我们为密集区间图制定了图极限理论。所发展的理论不同于通常将图形极限描述为单位平方上的对称函数W（x，y）的情况，其中x和y在间隔（0，1）上是均匀的。相反，我们固定W并更改坐标x和y的基本分布。我们找到的选择使我们的局限性是连续的。给出了与随机间隔图的连接，包括一些示例。我们还显示了间隔图的色数和团数的连续性结果。对于一般的图形极限，给出了一些关于极限描述唯一性的结果。