Packing triangles in bounded degree graphs
Information Processing Letters
Solving large FPT problems on coarse-grained parallel machines
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
Kernelization: New Upper and Lower Bound Techniques
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
Discrete Optimization
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Cluster Editing: Kernelization Based on Edge Cuts
Algorithmica - Special Issue: Parameterized and Exact Computation, Part I
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A linear vertex kernel for maximum internal spanning tree
Journal of Computer and System Sciences
Planar graph vertex partition for linear problem kernels
Journal of Computer and System Sciences
Note: Towards optimal kernel for connected vertex cover in planar graphs
Discrete Applied Mathematics
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We study the kernelization of the Edge-Disjoint Triangle Packing (Etp) problem, in which we are asked to find k edge-disjoint triangles in an undirected graph. Etp is known to be fixed-parameter tractable with a 4k vertex kernel. The kernelization first finds a maximal triangle packing which contains at most 3k vertices, then the reduction rules are used to bound the size of the remaining graph. The constant in the kernel size is so small that a natural question arises: Could 4k be already the optimal vertex kernel size for this problem? In this paper, we answer the question negatively by deriving an improved 3.5k vertex kernel for the problem.