A Linear Kernel for Planar Red-Blue Dominating Set

In the Red-Blue Dominating Set problem, we are given a bipartite graph $G = (V_B \cup V_R,E)$andaninteger$k$,andaskedwhether$G$hasasubset$D \subseteq V_B$ofatmost$k$\mathrm{"}blue\mathrm{"}verticessuchthateach\mathrm{"}red\mathrm{"}vertexfrom$V_R$isadjacenttoavertexin$D$. We provide the first explicit linear kernel for this problem on planar graphs, of size at most $43k$.