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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References
Diestel, R.: Graph Theory, Graduate Texts in Mathematics, 3rd edn., vol. 173. Springer, Heidelberg (2005), http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/GraphTheoryIII.pdf
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)
Fiorini, S., Joret, G., Pietropaoli, U.: Hitting Diamonds and Growing Cacti. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 191–204. Springer, Heidelberg (2010)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2006)
Fomin, F.V., Lokshtanov, D., Misra, N., Philip, G., Saurabh, S.: Hitting forbidden minors: Approximation and kernelization. In: STACS, pp. 189–200 (2011)
Hopcroft, J., Tarjan, R.: Algorithm 447: efficient algorithms for graph manipulation. Commun. ACM 16, 372–378 (1973), http://doi.acm.org/10.1145/362248.362272
Hüffner, F.: Algorithm engineering for optimal graph bipartization. J. Graph Algorithms Appl. 13(2), 77–98 (2009)
Kakimura, N., Ichi Kawarabayashi, K., Kobayashi, Y.: Erdös-pósa property and its algorithmic applications: parity constraints, subset feedback set, and subset packing. In: SODA, pp. 1726–1736 (2012)
Lokshtanov, D., Saurabh, S., Sikdar, S.: Simpler Parameterized Algorithm for OCT. In: Fiala, J., KratochvÃl, J., Miller, M. (eds.) IWOCA 2009. LNCS, vol. 5874, pp. 380–384. Springer, Heidelberg (2009)
Loksthanov, D., Narayanaswamy, N.S., Raman, V., Ramanujan, M.S., Saurabh, S.: Faster Parameterized Algorithms using Linear Programming. Ar**v e-prints (March 2012)
Reed, B.A., Smith, K., Vetta, A.: Finding odd cycle transversals. Oper. Res. Lett. 32(4), 299–301 (2004)
Thomassé, S.: A quadratic kernel for feedback vertex set. In: SODA, pp. 115–119 (2009)
Thomassen, C.: On the presence of disjoint subgraphs of a specified type. Journal of Graph Theory 12(1), 101–111 (1988)
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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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