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DAM
2007

Tree-edges deletion problems with bounded diameter obstruction sets

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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.
Dekel Tsur
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where DAM
Authors Dekel Tsur
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