## Abstract

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.

Original language | English |
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Pages (from-to) | 1275-1293 |

Number of pages | 19 |

Journal | Discrete Applied Mathematics |

Volume | 155 |

Issue number | 10 |

DOIs | |

State | Published - 15 May 2007 |

## Keywords

- Graph algorithms
- Subgraph isomorphism

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics