Journal of the ACM (JACM)
Vertex cover: further observations and further improvements
Journal of Algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Improved induced matchings in sparse graphs
Discrete Applied Mathematics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Planar graph vertex partition for linear problem kernels
Journal of Computer and System Sciences
Parameterized Complexity
A 9k kernel for nonseparating independent set in planar graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
A 9k kernel for nonseparating independent set in planar graphs
Theoretical Computer Science
Towards optimal kernel for edge-disjoint triangle packing
Information Processing Letters
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We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP@?coNP/poly), for planar graphs Guo and Niedermeier [ICALP'08] showed a kernel with at most 14k vertices, subsequently improved by Wang et al. [MFCS'11] to 4k. The constant 4 here is so small that a natural question arises: could it be already an optimal value for this problem? In this paper we answer this question in the negative: we show a 113k-vertex kernel for Connected Vertex Cover in planar graphs. We believe that this result will motivate further study in the search for an optimal kernel. In our analysis, we show an extension of a theorem of Nishizeki and Baybars [Takao Nishizeki, Ilker Baybars, Lower bounds on the cardinality of the maximum matchings of planar graphs, Discrete Mathematics 28 (3) (1979) 255-267] which might be of independent interest: every planar graph with n"="3 vertices of degree at least 3 contains a matching of cardinality at least n"="3/3.