A linear kernel for planar red–blue dominating set

Abstract

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 43k.