Tight Bounds for Visibility Matching of f-Equal Width Objects

Let s denote a compact convex object in IR. The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f . A set of disjoint convex compact objects in IR is of equal f -width if there exists a direction f such that every pair of objects have equal f -width. A visibility matching, for a set of equal f -width objects is a matching using non-crossing lines of site in the visibility graph of the set. In this note we establish tight bounds on the size of a maximal visibility matching for a set of f -equal width objects by showing that ⌊