Geodesic
An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 55-65

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Given a graph G = (V,E), the task in the vertex cover P3(VCP3) 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 VCP3 problem 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 VCP3 problem 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 VCP3 problem on planar graphs.
Keywords: combinatorial optimization, vertex cover P3 problem, branch- width, planar graphs, EPTAS 
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Tu, Jianhua; Shi, Yongtang. An Efficient Polynomial Time Approximation Scheme for the Vertex Cover P3 Problem on Planar Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 55-65. http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a5/