Abstract. We present new kernelization results for the s-cycle transversal problem for s > 3. In particular, we show a 6k2 kernel for 4-cycle transversal and a O(ks−1 ) kernel...
We consider the problem of finding a k-edge transversal set that covers all (simple) cycles of length at most s in a planar graph, where s ≥ 3 is a constant. This problem, refe...
The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite by deleting at most k of its vertices. In a breakthrough result Reed, Smith, and Vetta (Op...
We study the ratio between the minimum size of an odd cycle vertex transversal and the maximum size of a collection of vertex-disjoint odd cycles in a planar graph. We show that th...
We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of "small" length k in a given graph. The instance f...