Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
An 8-Approximation Algorithm for the Subset Feedback Vertex Set Problem
SIAM Journal on Computing
A Polyhedral Approach to the Feedback Vertex Set Problem
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Min-Max Theorem on Feedback Vertex Sets
Mathematics of Operations Research
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
On the odd-minor variant of Hadwiger's conjecture
Journal of Combinatorial Theory Series B
Note: Note on coloring graphs without odd-Kk-minors
Journal of Combinatorial Theory Series B
Notes: Packing cycles through prescribed vertices
Journal of Combinatorial Theory Series B
Subset feedback vertex set is fixed-parameter tractable
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
Graph Minors. XXII. Irrelevant vertices in linkage problems
Journal of Combinatorial Theory Series B
Parameterized Complexity
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We investigate generalizations of the following well-known problems in the framework of parameterized complexity: the feedback set problem and the cycle packing problem. Our problem setting is that we are given a graph and a vertex set S called ''terminals''. Our purpose here is to consider the following problems:1.The feedback set problem with respect to the terminals S. We call it the subset feedback set problem. 2.The cycle packing problem with respect to the terminals S, i.e., each cycle has to contain a vertex in S (such a cycle is called an S-cycle). We call it the S-cycle packing problem. We give the first fixed parameter algorithms for the two problems. Namely;1.For fixed k, we can either find a vertex set X of size k such that G-X has no S-cycle, or conclude that such a vertex set does not exist in O(n^2m) time, where n is the number of vertices of the input graph and m is the number of edges of the input graph. 2.For fixed k, we can either find k vertex-disjoint S-cycles or conclude that such k disjoint cycles do not exist in O(n^3) time.