Listing minimal edge-covers of intersecting families with applications to connectivity problems Original Research Article

Let image be a directed/undirected graph, let image, and let image be an intersecting family on image (that is, image for any intersecting image) so that image and image for every image. An edge set image is an edge-cover of image if for every image there is an edge in image from image to image. We show that minimal edge-covers of image can be listed with polynomial delay, provided that, for any image the minimal member of the residual family image of the sets in image not covered by image can be computed in polynomial time. As an application, we show that minimal undirected Steiner networks, and minimal image-connected and image-outconnected spanning subgraphs of a given directed/undirected graph, can be listed in incremental polynomial time.