Vertex Bisection is Hard, too

We settle an open problem mentioned in Diaz, Petit, and Serna: A survey of graph layout problems (ACM Computing Surveys 34:313–356, 2002). Of eight objectives considered in that survey, only the complexity status of minimum vertex bisection is listed as unknown. We show that both minimum and maximum vertex bisection are NP-hard, but polynomially solvable on special graph classes such as hypercubes and trees. Submitted: December 2005 Reviewed: April 2006 Revised: April 2007 Accepted: February 2009 Final: February 2009 Published: April 2009 Article type: Concise paper Communicated by: S. Albers E-mail addresses: [email protected] (Ulrik Brandes) [email protected] (Daniel Fleischer) 120 U. Brandes, D. Fleischer Vertex Bisection