  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.
