Algorithms for deletion problems on split graphs

In the Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems the input is a split graph $G$ and an integer $k$, and the goal is to decide whether there is a set $S$ of at most $k$ vertices such that $G-S$ is a block graph and $G-S$ is a threshold graph, respectively. In this paper we give algorithms for these problems whose running times are $O^*(2.076^k)$ and $O^*(2.733^k)$, respectively.