Polynomial-time recognition and maximum independent set in Burling graphs

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.