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(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.)
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Misra, P., Raman, V., Ramanujan, M.S., Saurabh, S. (2012). Parameterized Algorithms for Even Cycle Transversal . In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_19
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DOI: https://doi.org/10.1007/978-3-642-34611-8_19
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