The Burling sequence is a sequence of triangle-free graphs of increasing chromatic number. Each of them is isomorphic to the intersection graph of a set of axis-parallel boxes in $R^3$. These graphs were also proved to have other geometrical representations: intersection graphs of line segments in the plane, and intersection graphs of frames, where a frame is the boundary of an axis-aligned rectangle in the plane. We call Burling graph every graph that is an induced subgraph of some graph in the Burling sequence. We give five new equivalent ways to define Burling graphs. Three of them are geometrical, one is of a more graph-theoretical flavour and one is more axiomatic.

翻译：Burling序列是色数递增的无三角形图序列，其中每个图都同构于$\mathbb{R}^3$中一组轴平行盒的交图。这些图也被证明具有其他几何表示形式：平面中线段的交图，以及框架（即平面中轴对齐矩形的边界）的交图。我们将Burling序列中任何图的导出子图称为Burling图。本文给出了五种定义Burling图的新等价方式：其中三种基于几何性质，一种更具图论特征，另一种则更偏向公理化表述。