A Simple $$(2+\epsilon )$$-Approximation Algorithm for Split Vertex Deletion

A split graph is a whose vertex set can be partitioned into clique and stable set. Given G weight function \(w: V(G) \rightarrow \mathbb {Q}_{\ge 0}\), the Split Vertex Deletion (SVD) problem asks to find minimum of vertices X such that \(G-X\) graph. It easy show if only it does not contain 4-cycle, 5-cycle, or two edge matching as an induced subgraph. Therefore, SVD admits 5-approximation algorithm. On other hand, for every \(\delta >0\), admit \((2-\delta )\)-approximation algorithm, unless P = NP Unique Games Conjecture fails.