Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
An 8-approximation algorithm for the subset feedback vertex set problem
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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)
On the odd-minor variant of Hadwiger's conjecture
Journal of Combinatorial Theory Series B
Notes: Packing cycles through prescribed vertices
Journal of Combinatorial Theory Series B
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Packing cycles with modularity constraints
Combinatorica
Fixed-parameter tractability for the subset feedback set problem and the S-cycle packing problem
Journal of Combinatorial Theory Series B
Disjoint cycles intersecting a set of vertices
Journal of Combinatorial Theory Series B
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The well-known theorem of Erd驴s-Pósa says that a graph G has either k disjoint cycles or a vertex set X of order at most f(k) for some function f such that G\X is a forest. Starting with this result, there are many results concerning packing and covering cycles in graph theory and combinatorial optimization.In this paper, we discuss packing disjoint S-cycles, i.e., cycles that are required to go through a set S of vertices. For this problem, Kakimura-Kawarabayashi-Marx (2011) and Pontecorvi-Wollan (2010) recently showed the Erd驴s-Pósa-type result holds. We further try to generalize this result to packing S-cycles of odd length. In contrast to packing S-cycles, the Erd驴s-Pósa-type result does not hold for packing odd S-cycles. We then relax packing odd S-cycles to half-integral packing, and show the Erd驴s-Pósa-type result for the half-integral packing of odd S-cycles, which is a generalization of Reed (1999) when S=V. That is, we show that given an integer k and a vertex set S, a graph G has either 2k odd S-cycles so that each vertex is in at most two of these cycles, or a vertex set X of order at most f(k) (for some function f) such that G\X has no odd S-cycle.