A linear kernel for planar red–blue dominating set
Résumé
In the Red-Blue Dominating Set problem, we are given a bipartite graph $G=(VB∪VR,E)$ and an integer $k$, and asked whether G has a subset $D⊆VB$ of at most $k$ "blue" vertices such that each "red" vertex from $VR$ is adjacent to a vertex in $D$. We provide the first explicit linear kernel for this problem on planar graphs, of size at most 46k.