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A subset F of vertices of a graph G is called a vertex cover Pt (VCPt) set if every path of order t in G contains at least one vertex from F. The vertex cover Pt (VCPt) problem is to find a minimum VCPt set in a graph. The VCPt problem is NP-complete for any integer t≥2. In this paper, we restrict our attention to the VCP4 problem and present an FPT algorithm with runtime O∗(3k) for the VCP4 problem...
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