A faster FPT algorithm for Bipartite Contraction

The Bipartite Contraction problem is to decide, given a graph G and a parameter k, whether we can obtain a bipartite graph from G by at most k edge contractions. The fixed-parameter tractability of the problem was shown by Heggernes et al. [13], with an algorithm whose running time has double-exponential dependence on k. We present a new randomized FPT algorithm for the problem, which is both conceptually simpler and achieves an improved 2O(k2)nm running time, i.e., avoiding the double-exponential dependence on k. The algorithm can be derandomized using standard techniques. •We present an improved FPT algorithm for the Bipartite Contraction problem.•The running time improves on an earlier double-exponential algorithm by Heggernes et al. (2011).•The algorithm uses important separators and randomized coloring in a nontrivial way.