Theory of Computing ------------------- Title : Simple Proof of Hardness of Feedback Vertex Set Authors : Venkatesan Guruswami and Euiwoong Lee Volume : 12 Number : 6 Pages : 1-11 URL : https://theoryofcomputing.org/articles/v012a006 Abstract -------- The Feedback Vertex Set problem (FVS), where the goal is to find a small subset of vertices that intersects every cycle in an input directed graph, is among the fundamental problems whose approximability is not well understood. One can efficiently find an $\widetilde{O}(\log n)$-factor approximation, and efficient constant- factor approximation is ruled out under the Unique Games Conjecture (UGC). We give a simpler proof that Feedback Vertex Set is hard to approximate within any constant factor, assuming UGC.