Improved Kernels for Several Problems on Planar Graphs

In this paper, we study the kernelization of the Induced Matching problem on planar graphs, the Parameterized Planar 4-Cycle Transversal problem and the Parameterized Planar Edge-Disjoint 4-Cycle Packing problem. For the Induced Matching problem on planar graphs, based on Gallai-Edmonds structure, a kernel of size 26k is presented, which improves the current best result 28k. For the Parameterized Planar 4-Cycle Transversal problem, by partitioning the vertices in given instance into four parts and analyzing the size of each part independently, a kernel with at most \(51k-22\) vertices is obtained, which improves the current best result 74k. Based on the kernelization process of the Parameterized Planar 4-Cycle Transversal problem, a kernel of size \(51k-22\) can also be obtained for the Parameterized Planar Edge-Disjoint 4-Cycle Packing problem, which improves the current best result 96k.

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