A Linear Kernel for Planar Red-Blue Dominating Set

TL;DR

This paper presents the first explicit linear kernel of size at most 43k for the Red-Blue Dominating Set problem on planar graphs, improving kernelization bounds in parameterized complexity.

Contribution

It introduces the first explicit linear kernel for the problem on planar graphs, with a size bound of 43k, advancing kernelization techniques.

Findings

Linear kernel of size at most 43k for planar graphs

First explicit kernel for Red-Blue Dominating Set on planar graphs

Improved bounds in parameterized complexity

Abstract

In the Red-Blue Dominating Set problem, we are given a bipartite graph $G = (V_B \cup V_R,E)$ and an integer $k$, and asked whether $G$ has a subset $D \subseteq V_B$ of at most $k$ "blue" vertices such that each "red" vertex from $V_R$ is adjacent to a vertex in $D$. We provide the first explicit linear kernel for this problem on planar graphs, of size at most $43k$.