Parameterized algorithms for even cycle transversal

Abstract

We consider a decision version of the problem of finding the minimum number of vertices whose deletion results in a graph without even cycles. While this problem is a natural analogue of the Odd Cycle Transversal problem (which asks for a subset of vertices to delete to make the resulting graph bipartite), surprisingly this problem is not well studied. We first observe that this problem is NP-complete and give a constant factor approximation algorithm. Then we address the problem in parameterized complexity framework with the solution size k as a parameter. We give an algorithm running in time O (2 O(k)) for the problem and give an O(k 2) vertex kernel. (We write O (f(k)) for a time complexity of the form O(f(k)n O(1)), where f (k) grows exponentially with k.) © 2012 Springer-Verlag Berlin Heidelberg.