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24(3), pp. : Parallel repetition in projection games and a concentration bound. : A parallel repetition theorem. SIAM J. Comput. 27(3), 763–803 (1998) The Curse of Connectivity: t-Total Vertex (Edge) Cover Henning Fernau1 , Fedor V. in Abstract. We investigate the eﬀect of certain natural connectivity constraints on the parameterized complexity of two fundamental graph covering problems, namely k-Vertex Cover and k-Edge Cover. Speciﬁcally, we impose the additional requirement that each connected component of a solution have at least t vertices (resp.
An approach similar to the one used in Section 2 results in an FPT algorithm that runs in polynomial space: Theorem 6. [ ] t-tec can be solved in time O∗ 2O(k) space. 4 time in polynomial Conclusion We investigated the parameterized complexity of two problems, namely t-total vertex cover and t-total edge cover, obtained by imposing certain connectivity constraints on two classical problems, namely k-Vertex Cover and k-Edge Cover, respectively. We showed that for any t ≥ 2 the t-total vertex cover problem has no polynomial-size kernel unless PH collapses.
Sanders, P. ) ESA 2009. LNCS, vol. 5757, pp. 635–646. Springer, Heidelberg (2009) 7. : Vertex Cover: Further observations and further improvements. Journal of Algorithms 41(2), 280–301 (2001) 8. : Improved parameterized upper bounds for Vertex Cover. , Urzyczyn, P. ) MFCS 2006. LNCS, vol. 4162, pp. 238–249. Springer, Heidelberg (2006) 9. : Introduction to Algorithms, 2nd edn. The MIT Press, Cambridge (2001) 10. : Graph Theory, 3rd edn. Springer, Heidelberg (2005) 11. : Incompressibility through Colors and IDs.