  In this paper, we consider the following two problems: (i) Deletion
Blocker($\alpha$) where we are given an undirected graph $G=(V,E)$ and two
integers $k,d\geq 1$ and ask whether there exists a subset of vertices
$S\subseteq V$ with $|S|\leq k$ such that $\alpha(G-S) \leq \alpha(G)-d$, that
is the independence number of $G$ decreases by at least $d$ after having
removed the vertices from $S$; (ii) Transversal($\alpha$) where we are given an
undirected graph $G=(V,E)$ and two integers $k,d\geq 1$ and ask whether there
exists a subset of vertices $S\subseteq V$ with $|S|\leq k$ such that for every
maximum independent set $I$ we have $|I\cap S| \geq d$. We show that both
problems are polynomial-time solvable in the class of co-comparability graphs
by reducing them to the well-known Vertex Cut problem. Our results generalize a
result of [Chang et al., Maximum clique transversals, Lecture Notes in Computer
Science 2204, pp. 32-43, WG 2001] and a recent result of [Hoang et al.,
Assistance and interdiction problems on interval graphs, Discrete Applied
Mathematics 340, pp. 153-170, 2023].
