Tree-edges deletion problems with bounded diameter obstruction sets

We study the following problem: Given a tree G and a finite set of trees H, find a subset O of the edges of G such that G − O does not contain a subtree isomorphic to a tree from H, and O has minimum cardinality. We give sharp boundaries on the tractability of this problem: The problem is polynomial when all the trees in H have diameter at most 5, while it is NP-hard when all the trees in H have diameter at most 6. We also show that the problem is polynomial when every tree in H has at most one vertex with degree more than 2, while it is NP-hard when the trees in H can have two such vertices. The polynomial time algorithms use a variation of a known technique for solving graph problems. While the standard technique is based on defining an equivalence relation on graphs, we define a quasiorder. This new variation might be useful for giving more efficient algorithm for other graph problems.

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Dekel Tsur
• Keywords: DAM 2007, Polynomial, Sharp Boundaries, Tree