A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a polynomial-time algorithm to decide whether a given graph is a Burling graph and if it is, to construct its strict frame representation. The representation then 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 $χ$-bounded.

翻译：Burling图是Burling构造的无三角形高色度图中某些图的诱导子图。等价地，Burling图是承认所谓严格框架表示的图。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，若是则构造其严格框架表示。该表示进而为Burling图中的最大独立集问题提供了多项式时间算法。由此，我们确立Burling图为首个已知的、在非χ-有界的前提下仍承认此类算法的遗传图类。