Connected (s, t)-Vertex Separator Parameterized by Chordality

We investigate the complexity of finding a minimum connected (s, t)vertex separator ((s, t)-CVS) and present an interesting chordality dichotomy: we show that (s, t)-CVS is NP-complete on graphs of chordality at least 5 and present a polynomial-time algorithm for (s, t)-CVS on chordality 4 graphs. Further, we show that (s, t)-CVS is unlikely to have δlog2− n-approximation algorithm, for any > 0 and for some δ > 0, unless NP has quasi-polynomial Las Vegas algorithms. On the positive-side of approximation, we present a d c 2 e-approximation algorithm for (s, t)CVS on graphs with chordality c ≥ 3. Finally, in the parameterized setting, we show that (s, t)-CVS parameterized above the (s, t)-vertex connectivity is W [2]-hard. Submitted: October 2012 Reviewed: April 2013 Revised: March 2014 Reviewed: October 2014 Revised: November 2014 Reviewed: April 2015 Revised: May 2015 Accepted: October 2015 Final: October 2015 Published: November 2015 Article type: Regular paper Communicated by: M. Fürer E-mail addresses: [email protected] (N. S. Narayanaswamy) [email protected] (N. Sadagopan) 550 Narayanaswamy and Sadagopan Connected (s, t)-Vertex Separator