A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. We provide a polynomial-time algorithm which decides whether a given graph is a Burling graph and if it is, constructs its intersection model by rectangular frames. That model enables a polynomial-time algorithm for the maximum independent set problem in Burling graphs. As a consequence, we establish Burling graphs as the first known hereditary class of graphs that admits such an algorithm while not being $\chi$-bounded.

翻译：Burling图是Burling构造的无三角形高色度图中某些图的导出子图。我们提出了一种多项式时间算法，用于判定给定图是否为Burling图，若是则通过矩形框架构建其交模型。该模型为Burling图中的最大独立集问题提供了多项式时间求解算法。由此，我们确立了Burling图作为首个已知的遗传图类，其在非χ有界条件下仍具备此类算法。