Facet-inducing inequalities with acyclic supports for the caterpillar-packing polytope

A caterpillar is a connected graph such that the removal of all its vertices with degree 1 results in a path. Given a graph G, a caterpillar-packing of G is a set of vertex-disjoint (not necessarily induced) subgraphs of G such that each subgraph is a caterpillar. In this work we consider the set of caterpillar-packings of a graph, which corresponds to feasible solutions of the 2-schemes strip cutting problem with a sequencing constraint (2-SSCPsc) presented by Rinaldi and Franz (Eur. J. Oper. Res. 183 (2007) 1371–1384). Facet-preserving procedures have been shown to be quite effective at explaining the facet-inducing inequalities of the associated polytope, so in this work we continue this issue by exploring such procedures for valid inequalities with acyclic supports. In particular, the obtained results are applicable when the underlying graph is a tree