Every graph admits an unambiguous bold drawing

Let r and w be a fixed positive numbers, w < r. In a bold drawing of a graph, every vertex is represented by a disk of radius r, and every edge by a narrow rectangle of width w. We solve a problem of van Kreveld [K09] by showing that every graph admits a bold drawing in which the region occupied by the union of the disks and rectangles representing the vertices and edges does not contain any disk of radius r other than the ones representing the vertices.