The size of bipartite graphs with a given girth
Journal of Combinatorial Theory Series B
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Maximum cuts and judicious partitions in graphs without short cycles
Journal of Combinatorial Theory Series B
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Finding next-to-shortest paths in a graph
Information Processing Letters
Graph Theory and Its Applications, Second Edition (Discrete Mathematics and Its Applications)
Graph Theory and Its Applications, Second Edition (Discrete Mathematics and Its Applications)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Decomposing a planar graph with girth 9 into a forest and a matching
European Journal of Combinatorics
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algorithmica - Parameterized and Exact Algorithms
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Approximating Maximum Subgraphs without Short Cycles
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Equitable list colorings of planar graphs without short cycles
Theoretical Computer Science
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Generating random graphs with large girth
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Kernelization for cycle transversal problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Kernelization for cycle transversal problems
Discrete Applied Mathematics
| Hi-index | 5.23 |
We consider the problem of finding a k-edge transversal set that intersects all (simple) cycles of length at most s in a planar graph, where s=3 is a constant. This problem, referred to as Small Cycle Transversal, is known to be NP-complete. We present a polynomial-time algorithm that computes a kernel of size 36s^3k for Small Cycle Transversal. In order to achieve this kernel, we extend the region decomposition technique of Alber et al. (2004) [1] by considering a unique region decomposition that is defined by shortest paths. Our kernel size is a significant improvement in terms of s over the kernel size obtained under the meta-kernelization framework by Bodlaender et al. (2009) [7].