New 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 the Gallai-Edmonds decomposition structure, a kernel of size 26k is presented, which improves the previous best result 28k. For the Parameterized Planar 4-Cycle Transversal problem, by partitioning the vertices in a given instance into several parts and analyzing the size of each part independently, a kernel with at most 51 k − 22 vertices is obtained, which improves the previous best result 74k. Based on the kernelization process of the Parameterized Planar 4-Cycle Transversal problem, a kernel of size 51 k − 22 can also be obtained for the Parameterized Planar Edge-Disjoint 4-Cycle Packing problem, which improves the previous best result 96k.

Authors

• Guanlan Tan
• Qilong Feng
• Beilin Zhuo
• Neng Huang
• Jianxin Wang

Keywords

• Kernelization
• Induced matching
• Gallai-Edmonds decomposition
• Cycle transversal