An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs

Given a graph G = (V,E), the task in the vertex cover P3(V C P3) problem is to find a minimum subset of vertices F ⊆ V such that every path of order 3 in G contains at least one vertex from F. The V C P3problem remains NP-hard even in planar graphs and has many applications in real world. In this paper, we give a dynamic-programming algorithm to solve the V C P3problem on graphs of bounded branchwidth. Using the dynamic programming algorithm and the Baker’s EPTAS framework for NP-hard problems, we present an efficient polynomial time approximation scheme (EPTAS) for the V C P3problem on planar graphs