Parameterized algorithms for even cycle transversal

Authors:
Pranabendu Misra;Venkatesh Raman;M. S. Ramanujan;Saket Saurabh
Affiliations:
Chennai Mathematical Institute, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India
Venue:
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2012

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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*(2O(k)) for the problem and give an O(k2) vertex kernel. (We write O*(f(k)) for a time complexity of the form O(f(k)nO(1)), where f (k) grows exponentially with k.)