Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
On the complexity of finding iso- and other morphisms for partial k-trees
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The maximum subforest problem: approximation and exact algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
A combinatorial and logical approach to linear-time computability
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Parameterized Complexity
On the approximability of the Maximum Agreement SubTree and Maximum Compatible Tree problems
Discrete Applied Mathematics
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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.