Theoretical Computer Science 487 (2013) 103–105 Contents lists available at SciVerse ScienceDirect Theoretical Computer Science journal homepage: www.elsevier.com/locate/tcs Corrigendum Corrigendum to ‘‘Cycle transversals in perfect graphs and cographs’’ [Theoret. Comput. Sci. 469 (2013) 15–23] Andreas Brandstädt a , Synara Brito b , Sulamita Klein c , Loana Tito Nogueira b , Fábio Protti b,∗ a Institut für Informatik, Universität Rostock, Germany b Instituto de Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil c DCC/IM and COPPE, Universidade Federal do Rio de Janeiro, Brazil article info Article history: Received 8 January 2013 Received in revised form 22 March 2013 Accepted 24 March 2013 Communicated by G.F. Italiano Keywords: Cycle transversals Cographs Feedback Vertex Set Perfect graphs abstract In this corrigendum we fix the proof of Theorem 1 in Brandstädt et al. (2013) [1]. © 2013 Elsevier B.V. All rights reserved. 1. Fixing the proof We present below a minor modification in the proof of the following theorem in [1]: Theorem 1. Let G be a bipartite graph with maximum degree four, and k be a positive integer. Then deciding whether G admits a cycle transversal of size at most k is NP-complete. Proof. The problem is clearly in NP. The hardness proof is a reduction from a special version of SAT, denoted here as 3-SAT 3 : each clause contains at most three literals, and each variable occurs exactly three times, twice positively and once negatively. The NP-completeness of this problem is a consequence of the results in [2,3]. Given an instance F of 3-SAT 3 with n variables x 1 , x 2 ,..., x n and m clauses C 1 , C 2 ,..., C m , we construct G by creating a bipartite subgraph G i for each variable x i , as in Fig. 1. Vertices a i and a ′ i represent the two positive occurrences of x i , and vertex a ′′ i represents its negative occurrence. Let T i denote a cycle transversal of G i . Clearly, |T i |≥ 3. We will assume that T i does not contain the subset {a i , a ′′ i } or the subset {a ′ i , a ′′ i }. The idea is to avoid choosing vertices a i , a ′′ i (or a ′ i , a ′′ i ) simultaneously, because this implies |T i |≥ 4. Next, for each clause C j ,1 ≤ j ≤ m, we create a subgraph Z j isomorphic to an even cycle, according to the following rules: – if x i occurs in C j and C j ′ (j ≤ j ′ ) then a i ∈ V (Z j ) and a ′ i ∈ V (Z j ′ ); – if x i occurs in C j then a ′′ i ∈ V (Z j ); DOI of original article: http://dx.doi.org/10.1016/j.tcs.2012.10.030. ∗ Corresponding author. Tel.: +55 21 26295636. E-mail addresses: ab@informatik.uni-rostock.de (A. Brandstädt), sbrito@ic.uff.br (S. Brito), sula@cos.ufrj.br (S. Klein), loana@ic.uff.br (L.T. Nogueira), fabio@ic.uff.br, fabio@ic.uff.br (F. Protti). 0304-3975/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tcs.2013.03.022