Fig. 7

Five cases where two vertices are deleted in the same bag with \(d=1\). Bags are points in the line, and an interval covering all bags containing v is drawn for each v (with an equivalent coloring, see Proposition 1). Cases (a) to (d) can be safely avoided by applying the given transformations. In the example for case (e), however, it is necessary to delete both vertices u and v form a central bag. It is sufficient to avoid cases (a) and (b) in order to obtain an XP algorithm for d