Planar graph vertex partition for linear problem kernels

Jianxin Wang, Yongjie Yang, Jiong Guo, Jianer Chen

Abstract: A simple partition of the vertex set of a graph is introduced to analyze kernels for planar graph problems in which vertices and edges not in a solution have small distance to the solution. This method directly leads to improved kernel sizes for several problems, without needing new reduction rules. Moreover, new kernelization algorithms are developed for Connected Vertex Cover, Edge Dominating Set, and Maximum Triangle Packing problems, further improving the kernel sizes for these problems.