# Cycle Killer...Qu'est-ce que c'est? On the Comparative Approximability of Hybridization Number and Directed Feedback Vertex Set

@article{Kelk2012CycleKQ, title={Cycle Killer...Qu'est-ce que c'est? On the Comparative Approximability of Hybridization Number and Directed Feedback Vertex Set}, author={Steven M. Kelk and Leo van Iersel and Nela Lekic and Simone Linz and C{\'e}line Scornavacca and Leen Stougie}, journal={SIAM J. Discret. Math.}, year={2012}, volume={26}, pages={1635-1656} }

We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa $X$ has a constant factor polynomial-time approximation if and only if the problem of computing a minimum-size feedback vertex set in a directed graph (DFVS) has a constant factor polynomial-time approximation. The latter problem, which asks for a minimum number of vertices to be removed from a directed graph to transform it into a directed acyclic graph, is one of the…

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