Given n orthogonal line segments on the plane, their intersection graph is defined such that each vertex corresponds to a segment, and each edge corresponds to a pair of intersecting segments. Although this graph can have f~(n 2) edges, we show that breadth first search can be accomplished in O(n log n) time and O(n) space. As an application, we show that the minimum link rectilinear path between two points s and t amidst rectilinear polygonal obstacles can be computed in O(nlog n) time and O(n) space, which is optimal. We mention other related results in the paper. 