Graph decomposition is NPC - a complete proof of Holyer's conjecture
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An 8-Approximation Algorithm for the Subset Feedback Vertex Set Problem
SIAM Journal on Computing
Constant Ratio Approximations of the Weighted Feedback Vertex Set Problem for Undirected Graphs
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Packing cycles in undirected graphs
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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
Approximation algorithms for the loop cutset problem
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
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A classic theorem of Erdos and Posa states that there exists a constant c such that for all positive integers k and graphs G, either G contains k vertex disjoint cycles, or there exists a subset of at most cklogk vertices intersecting every cycle of G. We consider the following generalization of the problem: fix a subset S of vertices of G. An S-cycle is a cycle containing at least one vertex of S. We show that again there exists a constant c^' such that G either contains k disjoint S-cycles, or there exists a set of at most c^'klogk vertices intersecting every S-cycle. The proof yields an algorithm for finding either the disjoint S-cycles or the set of vertices intersecting every S-cycle. An immediate consequence is an O(logn)-approximation algorithm for finding disjoint S-cycles.