A bound on the treewidth of planar even-hole-free graphs

The class of planar graphs has unbounded treewidth, since the k×kk×k grid, ∀k∈N∀k∈N, is planar and has treewidth kk. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if GG is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.