, 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 [12]. 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

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