# Algorithms for deletion problems on split graphs

## TL;DR

This paper develops fixed-parameter algorithms for split graph deletion problems, specifically transforming split graphs into block or threshold graphs efficiently with exponential algorithms.

## Contribution

The paper introduces new algorithms with specific exponential running times for Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems.

## Key findings

- Algorithms run in $O^*(2.076^k)$ and $O^*(2.733^k)$ time
- Efficient fixed-parameter algorithms for split graph deletion problems
- Improved computational methods for graph modification problems

## Abstract

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.