, X 1 ? X 2 ) has no cycles and (g, h i ) is a b-characteristic of H i, Since Inc(Comp(t, X)

, It follows from the assumption that h(v, B) = h 1 (v, B) ? h 2 (v, B) for each

, Pair(H, B t \ X) and the (B t \ X)-block F of H containing B, F is partially label

, We consider F as the sum of

, Since each (g, h j ) is a b-characteristic of (H j , B tj \ X), (F ? H 1 , V (F ) ? (B t \ X)) and (F ? H 2 , V (F ) ? (B t \ X)) are block-wise partially label-isomorphic to g(v, B). Moreover, (F ?H 1 , V (F )?(B t \X)) and (F ?H 2 , V (F )?(B t \X)) are block-wise g(v, B)-compatible, because of the assumption that for each (w, B) ? Pair(t, X), h 1 (w, B)?h 2 (w, B) = ? and h(w, B) = h 1 (w, B) ? h 2

, This follows from the fact that (g, h j ) is a b-characteristic of

, XX:40 Generalized feedback vertex set problems on bounded-treewidth graphs

. Clique and . But, assuming the ETH holds, no such algorithm for Multicolored Clique exists . So we have the following: Theorem 25. Unless the ETH fails, there is no f (w)n o(w)-time algorithm for Bounded P-Component Vertex Deletion when P contains all chordal graphs

H. L. Bodlaender, M. Cygan, S. Kratsch, and J. Nederlof, Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth, Inform. and Comput, vol.243, pp.86-111, 2015.

H. L. Bodlaender, P. G. Drange, M. S. Dregi, F. V. Fomin, D. Lokshtanov et al., A c k n 5-Approximation Algorithm for, Treewidth. SIAM J. Comput, vol.45, issue.2, pp.317-378, 2016.

E. Bonnet, N. Brettell, O. Kwon, and D. Marx, Parameterized vertex deletion problems for hereditary graph classes with a block property, Graph-Theoretic Concepts in Computer Science (Proceedings of WG 2016, vol.9941, pp.233-244, 2016.

É. Bonnet, N. Brettell, O. Kwon, D. Marx, and X. X. , , p.41

B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Inform. and Comput, vol.85, issue.1, pp.12-75, 1990.

M. Cygan, F. V. Fomin, ?. Kowalik, D. Lokshtanov, D. Marx et al., Parameterized Algorithms, 2015.

M. Cygan, J. Nederlof, M. Pilipczuk, M. Pilipczuk, and J. M. Van-rooij, Wojtaszczyk. Solving connectivity problems parameterized by treewidth in single exponential time (extended abstract), 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science-FOCS 2011, pp.150-159, 2011.

P. G. Drange, M. S. Dregi, and P. Van-&apos;t-hof, On the computational complexity of vertex integrity and component order connectivity, Algorithms and computation, vol.8889, pp.285-297, 2014.

J. Enright and K. Meeks, Deleting edges to restrict the size of an epidemic: a new application for treewidth, Combinatorial Optimization and Applications, vol.9486, pp.574-585, 2015.

M. R. Fellows, F. V. Fomin, D. Lokshtanov, F. Rosamond, S. Saurabh et al., On the complexity of some colorful problems parameterized by treewidth, Information and Computation, vol.209, issue.2, pp.143-153, 2011.

F. V. Fomin, D. Lokshtanov, and S. Saurabh, Efficient computation of representative sets with applications in parameterized and exact algorithms, Proceedings of the TwentyFifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.142-151, 2014.

D. Lokshtanov, D. Marx, and S. Saurabh, Known algorithms on graphs on bounded treewidth are probably optimal, Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp.777-789, 2011.

D. Lokshtanov, D. Marx, and S. Saurabh, Lower bounds based on the Exponential Time Hypothesis, Bulletin of the EATCS, vol.105, pp.41-72, 2011.

D. Lokshtanov, D. Marx, and S. Saurabh, Slightly superexponential parameterized problems, Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp.760-776, 2011.

D. Marx, Can you beat treewidth? Theory of Computing, vol.6, pp.85-112, 2010.